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A 


NEW TREATISE 

ON THE 

USE OF THE GLOBES, 

OR, 

A PHILOSOPHICAL VIEW 


OB 

THE EARTH AND HEAVENS 


COMPREHENDING, 

An account of the Figure, Magnitude, and Motion of the Earth, the 
natural changes of its surface, caused by Floods, Earthquakes, etc. 
together w ith the Elementary Principles of Meteorology, 
and Astronomy, the Theory of the Tides, etc. 

PRECEDED BY 


An extensive Selection of Astronomical and other Definitions; and illustrated by a 
great variety of Problems and Cluestions, for the examination 
of the student, &c. 


DESIGNED FOR THE INSTRUCTION OF YOUTH. 

> ' 

> 'i i 

BY THOMAS KEITH, 

PRIVATE TEACHER OF MATHEMATICS, GEOGRAPHY, &C.. 


THE THIRD AMERICAN, FROM THE LAST LONDON 
IMPROVED EDITION. 


NEW-YORK: 

PUBLISHED BY SAMUEL WOOD & SONS, 
NO. 261, PEARL-STREET, 

And Samuel S. Wood & Co. No. 212, Market-st. 

BALTIMORE. 

wvwv\/w 

1819. 


f 


• • 






PREFACE. 


Amongst the various branches of science studied in our 
academies and places of public education, there are few of 
greater importance than that of the Use of the Globes. The 
earth is our destined habitation, and the heavenly bodies mea¬ 
sure our days and years by their various revolutions. With*, 
out some acquaintance with the different tracts of laud, the 
oceans, seas, &c. on the surfaces of the terrestrial globe, no in¬ 
tercourse could be carried o[i with the inhabitants of distant re¬ 
gions, and consequently, their manners, customs, &c. would be 
totally unknown to us. Though the different tracts of land, <fec. 
cannot be so minutely described on the surface of a terrestrial 
globe as on different maps; yet the globe shows the figure of 
the earth, and the relative situations of the principal places on 
its surface, more correctly than a map. Had the ancients paid 
no attention to the motions of the heavenly bodies, historical 
facts would have been given, without dates, and we should 
have neither dials, clocks, nor watches. To the celestial ob¬ 
servations of Eudoxus, Hipparchus, &c. w e are indebted for 
the knowledge of the precession of the equinoxes. Without 
some acquaintance with the celestial bodies, our ideas of the 
povrer and wisdom of the Creator would be greatly circum¬ 
scribed and confined. The learned and pious Dr. Watts ob¬ 
serves, “What wonders of wisdom are seen in the exact regu¬ 
larity of the revolutions of the heavenly bodies ! Nor was 
there ever any thing that has contributed to enlarge my ap¬ 
prehensions of the immense power of God, the magnificence of 
his creation, and his own transcendent grandeur, so much as the 
little portion of astronomy w hich I have been able to attain. 
And I would not only recommend it to young students, for the 
same purposes, but I would persuade all mankind, if it were 
possible, to gain some degree of acquaintance with the vast¬ 
ness, the distances, and the motions of the planetary worlds, 
on the same account.” 

Dr. Young in his Night Thoughts says, 

‘‘ An undevout Astronomer is mad.’^ 

There is scarcely a writer on the <lifferent branches of edu¬ 
cation w^ho has not expressly recommended the study of the 
Globes. Miltou observes, that “ Ere half the school auUiors 


PREFACE. 


iv 

be read, it will be seasonable for youtli to learn the use of the 
globes.” Yet notwithstanding the importance of the subject, it 
is entirely neglected in our public schools ; and iu many of 
our private academies, it has been frequently imperfectly 
taught; probably for want of a treatise sufficiently compre¬ 
hensive in its object, and illustrated by a suitable number of 
examples. 

There are several treatises on the globes extant, but they 
have been chiefly written by mathematical instrument makers,* 
or by teachers unacquainted with mathematics. The works 
of the former must be defective for want of practice in the 
art of teaching; and manj of the productions of the latter are 
too puerile and trifling to be iutro(iuced into a respectable aca¬ 
demy. Youth learn nothing elTectually but by frequent repi- 
tition; a multiplicity of examples, therefore, becomes absolute¬ 
ly necessary : but these examples should be so varied, and the 
mode of proposing the questions so diversified, as to give the 
scholar room for the exertion of his faculties, or otherwise no 
impression will remain on his mind. Treatises on the globes 
are generally either without any practical exercises ; or the 
exercises so similar, that when the pupil has finished one of 
them, the rest may be performed without the trouble of think¬ 
ing. Examples of this kind may serve to pass the time away, 
but they will never instruct the scholar. 


* The addition of a few wires, a semi-circle of brass, a particular 
kind of hour circle, &:c. which is of no other use on the globe than to en¬ 
hance the price thereof, has generally been a sufficient inducement for 
the instrument maker to publi.'«h a treatise explanatory of the use of 
such addition. The more simply the globes are fitted up, and the less 
they are encumbered with useless wires, &c. the more easily they will be 
understood by the generality of learners. The most important part of 
a globe IS its external surface : if the places on the terrestrial globe, and 
the stars on tbe celestial, be accurately laid down and distinctly and 
clearly engraven, it is of little consequence of what materials the frame 
is made. The best globes are those executed by Cary, ami the new 
British globes by Bardin, the plates of all other globes have been in 
common use above half a century (see page 155.) The new British 
globes, manufactured under the direction of Messrs. W. & S. Jones, are 
particularly recommended by Mr Vince, in vol. i. page 569 of his Com¬ 
plete .System of Astronomy, and were introduced into the Royal Ob- 
servatory by the late Dr. Maskelyne. 

Cary’s Globes, and the New British Globes, may be purchased at the 
shops of any of the principal Mathematical instrument makers in Lon¬ 
don. 

NOTICE.-—Very neat and correct Globes have been recently made 
in this country, which may be had, upon reasonable terms, of the pub¬ 
lishers of this work, at their Book-stores in New-Vork and Baltimore ; 
where the British Globes may also be obtained, of various sizes, from 
to !iil inches. 

NiwYork, 1819. 




PREFACE- 


V 


Had any mathematical writer of note furnished the student 
with a treatise on the globes, the following work would proba- 
bl} have never appeared ; but it rarely happens that the man 
of science, whose whole time is employed in abstruse research¬ 
es, wdl stof»p to the humble task of accommodating himself to 
the capacity ot a learner. To a man in the, habit of contem¬ 
plating the writings of a Newton, or travelling in the dry and 
difficult paths of abstract knowledge, a treatise on the globes is 
a mere play-thing, a trifle not worth notice; as at one glance 
he sees and comprehends every problem that can be perform¬ 
ed by them. Such a man would acquire no credit by writing 
a Treatise on the Globes; for, notwithstanding the utility of 
the subject, its simplicity would leave no room for him to dis¬ 
play his abilities; the task, tlierefore, necessarily devolves 
on writers of a more humble rank. 

The ensuing treatise has been formed entirely from the 
practice of Instruction, and is arranged in the following or¬ 
der. 

Part f. The contents of this part are enumerated in the 
first, page of the work. The definitions are very extensive, 
and, it is hoped, sufficiently plain and clear. Where the name 
of any ancient author occurs, the time in which he flourished, 
anil his country, are generally mentioned in a note; this prac¬ 
tice is followed throughout the book. The table of climates 
has been newly calculated, and the principle of calculation is 
given at full length. The first chapter likewise contains a ta¬ 
ble of the constellations, with a fabulous history of several of 
them ; the Greek alphabet, &C. If the definitions, geographical 
theorems, &:c. in this chapter be well explained by the tutor, it is 
presumed that the scholar will derive considerable advantage. 
The second chapter contains the general properties of matter, and 
the laws of motion, as preparatory to the reading of the third 
and fourth chapters; which would otherwise be less intelligible. 
To the third ?lQ(\ fourth chapters are added some useful notes, 
which ought to be attended to by those students who are ac¬ 
quainted with arithmetic. The fifth chapter treats of springs, 
rivers, and the saltness of the sea ; the sixth of the tides; and 
the seventh of earthquakes, &c. with their eflects and causes. 
The eight chapter contains, in a small compass, the principal 
theories of the earth. The subject of the ninth chapter is the 
atmosphere, and of the tenth, meteorology. From each of these 
chapters, it is hoped, the student will derive some useful in¬ 
formation. 

It has not been usual to introduce several of the aforesaid 
subjects into a Treatise on the Globes. An intelligent reader 
will, however, readily admit them to be less extraneous, equally 
entertaining, and more instructive than scraps of poetry, hist or- 


V 


PREFACE. 


ical auecdotes, &c. with which some of our Treatises on the 
Globes abound. Poetical scraps seldom elucidate either maih- 
ematical or philosophical subjects, and ^eiieially divert the 
attention of the student from the main object of his pursuit. 

Part II. This part comprehends the solar system, and 
such other parts of astronomy as are absolutely necessary td 
be clearly understood by the young student, before he atten.pts 
to solve many of the problems in the succeeding parts of the 
book. The object in learning the Use of the Globes should be 
to illustrate some of the most important branches of geography 
and astronomy ; and this object cannot be obtained by merely 
twirling the globe round and working a few problems, without 
understanding the principles on which their solutions are found¬ 
ed, Lessons thoroughly explained and clearly und< rstood 
make a lasting impression on the student's memor}% and will 
enable him, uot only to solve such problems as be may meet 
with in books on the Globes, but to frame several new problems 
himself, and to solve others which he never heard of before. 

In the notes attached to this part of the following work, the 
distances, magnitudes, &c. of the planets, are all accurately 
calculated. This laborious task the author would gladly have 
avoided, but he found the accounts of the distances, magnitudes, 
&c. of the planets so variable and contradictory, even in as¬ 
tronomical works of repute, and frequently in the same author, 
that he conceived such notes as he has introduced would be 
very useful to a learner. 

Part III. Contains an extensive collection of Problems; 
illustrated by a great number of useful examples, many of 
which are elucidated with notes of considerable importance. 

Part IV. Comprehends a miscellaneous selection of Prob¬ 
lems, Questions for the examination of the student, &c. togeth¬ 
er with an extensive table of the latitudes and longitudes of 
places. This table will be found to be more correct than the 
generality of Tables of a similar nature 

To Conclude. The author apprehends that he has omit¬ 
ted nothing of importance that particularly relates to the sub¬ 
ject, and he hopes at the same time, that this work will be 
found to contain little or no extraneous matter. He has en¬ 
deavoured to supply the young student with a Treatise ou 
the Globes, which n)ay not be unworthy of attention, as a w'ork 
of science, yet sufficiently plain and intelligible. He is aware 
that the work would have been preferred by many teachers 
(on account of its cheapness) had all the matter from nage 39 
to 163 been left out, as it w ould then have contained the mere 
definitions and problems ; yet in this state (though it would 
have been more comprehensive than almost any other Trea¬ 
tise) it would certainly have been very defective, 1805. 


PREFACE 


TO 

THE THIRD LONDON EDITION, 


A NEW plate was delineated, for the second edition of this 
work, which was published in the year 1808, showing the path 
of the planet Jupiter in the zodiac, for the year 1811, togeth¬ 
er with the constellations and principal stars through which he 
passes, agreeable to their appearance in the heavens. Delin¬ 
eations of this kind will not only prove amusing, but instruc¬ 
tive to the scholar, as they give a more correct idea of the rela¬ 
tive situations of the stars on the globe. 

By laying down on paper all the principal constellations 
from the celestial globe, as directed in Problem CII; rejecting 
such stars as are smaller than those of the fourth magnitude, 
and those constellations which do not come above the horizon, 
the young student will soon render the appearance of the heav¬ 
ens familiar to him. 

This third edition has been carefully revised, and some 
useful additional matter has been introduced, with the design 
of rendering the work as complete, and comprehensive, as the 
nature of the subject will admit. 

Norfolk-street, Fitzroy-square, 

London, 1811. 



CONTENTS 


1* 0 

PART I. 


XINES OlV THE AETXFICIAL 

GLOBES. ASTRONOMICAL 

DEEINI- 

TioNs, &;c. 

m 


• 

• • • 

Page 1 to S9. 

Aberration, 

- 

- 

SSjCetus, 


- 

32 

Acronycal, 

- 

- 

22|Centaurus 


- 

S3 

Almacantars, 

- 

- 

9 

Circles, Great - 


- 

3 

Altitude, 

-' 

- 

10 

Circles, Small 


- 

3 

Amplitude, 

- 


11 

Climate and Tables, 


- 

16 

Amphiscii, 

- 

- 

18 

Colures, 


- 

10 

Andromeda, 

- 

- 

SO 

Coma Berenices 


- 

29 

Angle of Position, 

- 

> 

21 

Compass, Mariner’s 


- 

8 

Antinbus, 

- 

> 

29 

Constellation, 


- 

22 

Antipodes, 

- 

- 

19 

Constellations, a table of 

2S to 26 

Aritceci, 



19 

Constellations, Alphabetical 


Aphelion 

- 


S7 

List of, &c. - 

- 

26 to 28 

Apogee, 

- 


S7 

Constellations, Histo 

rical ac- 


Apparent Noon, 

- 


12 

c>»unt of 


28 to S4 

Apsides, 

- 


S7 

Cor Caroli, 

- 


SI 

Aquila, 

- 


29 

Corvus, 

- 


S3 

Ara, 

- 


SS 

Corona Borealis, 

- 


SO 

Argo Navis, 

- 


S4 

Cosraical 

- 


22 

Ascension, Right 

- 


19 

Crepusculum, 

- 


20 

— ' —, Oblique 

- 


19 

Crux, 

- 


S3 

Ascensional Difference, 


19 

Culminating Point, 

- 


12 

Ascii, 

- 


18 

Cvgnus, 

- 


SI 

Aspect of the Planets, 


S6 





Asterion et Chara, 

- 


29 

Day, Astronomical 

- 


13 

Auriga, 

- 


S2 

-, Artificial - 

- 


ib. 

Azimuth, - 

- 


11 

-Civil 

. 


ib. 

Azimuth, or Vertical Circles, 

10 

——, Mean Polar, 

• 


12 

Axis of the Earth, 

- 

- 

c> 

—Solar True 

. 


ib. 





-, Siderial 

• 


IS 

Bayer’s characters of the stars. 

S4 

Declination, 

. 


4 

Bootes, 

- 

- 

29 

Delphinus, 

- 


SO 





Descensional Difference, 


19 

Canes Venatici, 


- 

29 

Digit, 

. 


S7 

Cardinal Points, 


• 


Direct, 

. 


37 

Cassiopeia, 


- 

SI 

Dif*c, 

- 


ST 

Cameleopardalus, 


- 

3. 

Diurnal Arch, - 

. 


S8 

Canis Minor, 


- 

S3 

Draco, 

• 


SI 

Canis Major, 


- 

3,8 





C'elestial Globe, 


- 

2 

Eccentricity, - 

. 


37 

Cepheus, - 


- 

Si 

Eclipse of the Sun, 

• 


38 

Centrifugal Force, 


- 

38 

-, of the Moon 



S8 

Centripetal Force, 


- 

3? 

Ecliptic 


. 

S 

Cerberus, 



SO 

Elongation, 

- 

38 & 153 












CONTENTS, ix 




Page 


Page 

Equator, - 


3 

Nebulous Stars, 


34 

Equation of Time 


12 

Nocturnal Arch, 


38 

Equinoctial Points, 


7 

Nodes of a Planet, 


36 

Equulus, - 


29 

Noon, Apparent 


12 

Ei’idanus, 


32 

Noon, True or Mean, 


12 

Eudoxus (note) 


14 







Oblique Ascension, - 


19 

Fixed stars. 

- 22 

, & 155 

Oblique Descension, - 


19 

Force, Centrifugal 


38 

Occultatiun, - - 


3T 

Force, Centripetal 


38 

Orbit of a Planet, 


36 




Orion, - - - 


32 

Galaxy, - 


34 




Geocentric, 

1% 

S7 

Parallels of Celestial Latitude, 

10 

Globe, Celestial 


2 

Parallels of Declination, 


10 

Globe, I’eiTestrial 


1 

Parallels of Latitude, 


5 

Great Circles, - 


3 

Pegasus, - - - 


30 

Greek Alphabet, 


35 

Perigee, - - - 


3T 




Perihelion, 


3T 

Heliacal, - 


22 

Periscii, - - - 


19 

Heliocentric, 


37 

Paeiioeci, - - - 


19 

Hemisphere, 


8 

Perseus, - - - 


31 

Hercules, 


SO 

Piscis Australis, 


32 

Hesiod, (note) 


14 

Planets, - . - 

35 Sc 36 

Heteroscii, 


18 

Pliny, (note) 


14 

Hipparchus, (note) 


10 

Poetical rising and setting 



Historical Account of the 


of the Stars, - 


22 

Zodiacal Signs, 


28 

Points, Cardinal 

% 

7 

Horizon, - 


6 

Polar Circles, - 


5 

Horizon, wooden 


6& 7 

Polar Distance, 


11 

Hour Circle, 


5 

Polar Star, (note) 


2 

Hour Circles, 


11 

Poles of the Earth, - 


2 

Hydra, 


33 

Pole of any Circle, 


7 

Lacerta, - 


31 

Positions of the Sphere, 


IS 

Latitude of a place. 


9 

Precession of the Eciuinoxes, 

14 

Latitude of a Planet or Star, 9 

Prime Vertical, 


10 

Leo Minor, 


29 




Lepus, 


33 

Quadrant of Altitude, 


9 

Line of the Apsides, 


37 




Lines of Longitude, 


3 

Refraction, 


20 

Longitude of a place, 

9 

Retrograde, 


31 

Longitude of a Planet or Star, 9 

Rhumbs, 


21 

Lynx, 

- 

32 

Right Ascension, 


19 

Lyra, 

- 

SO 

Robur Caroli, 


34 

Mariner’s Compass, 

. 

8 

Sagitta, - - - 


30 

Matter, General Propertie 


Scutum Sobieski, 


29 

of, &c. - 

- 

42 

rierpens. 


29 

Meridians, 


3 

Serpentarius, 


29 

Meridian, Brazen 

. 

2 

Sextans, 


33 

Meridian, First, 

. 

3 

'^ix o’clock Hour Line, 


11 

Microscopium, 

- 

33 

Small Circles, 


3 

Milky Way, 

- 

34 

J'phere, Positions of - 


IS 

Mons Msenalus, 

- 

28 

Solstitial Points, 


8 

Monoceros, 

- 

S3 

Stationary 


37 

Motion, General laws of 

45 




Motion, Compound, &c. 

46 

Taurus Poniatowski, 


29 

Nadir, * 


7 

Triangulum, 


31 


2 









X 


CONTENTS. 


Transit, 

Tropics, - - 

Twilight, 

Variation of the Compass, 
Vertical Circles, 

Via Lactea, 

Vulpecula et Anser, 


Page 


37 

5 

20 

8 

10 

34 

30 

31 


Year, Siderial, • 

Year, Solar 

Zenith, 

Zenith Distance, 

Zodiac, - - - 

Zodiacal Signs, 

Zodiacal Signs, Historical Ac¬ 
count thereof, 

Zones, - - - 


Ursa Major, 

Geographical Theorems, - . . . . 

Of the General Properties of Matter and the Laws of Motion, 

Of the Figure of the earth and its magnitude. 

Of the Diurnal and Annual Motion of the Earth, 

Of the Origin of "prings and Rivers, and of the saltness of the Sea, 
Of the Flux and Reflux of the Tides, 

Of the natural Changes of the Earth, caused by Mountains, Floods, 


jPage 

U 

14 

7 

10 

4 

4 

28 

18 

39 

42 

52 

58 

67 

71 


Volcanoes, and Earthquakes, 

• • 

• 

81 

Hypotheses of the Antediluvian World, and the Cause of Noah’s 

Flood, 

. 



91 

Dr. Burnet’s Theory, 

. 



91 

Dr. Woodward’s Theory, 

. 



93 

Mr. Whiston’s Theory, 

. 



94 

Buffon’s Theory, 

.• 


• 

. 96 

Dr. Hutton’s Theory, 

. 



. 99 

Mr. Whitehurst’s Theory. 

. 

. . 


102 

Of the Atmosphere, Air, Winds and Hurricanes, 


104 

Of Vapours, Fogs, Mists, Clouds, Dew, &c. 


113 

Fogs and Mists, 

. 

• 


113 

Clouds, 

. 

• • 


113 

Dew, 

. 

* 


114 

Rain, 

. 

• 

• 

114 

Snow and Hail, 

. 



115 

Thunder and Lightning, 

. 



116 

The Falling Stars, . 

. 



117 

Of the Ignis Fatuus, . 

# 

• • 


117 

Of the Aurora Borealis, 

, 

• ^ 


. 118 

Of the Rainbow, 

. 

• 


119 



PART II. 


Of the Solar System, 

Of the Sun, - ... 

Of Mercury, .... 

Of Venus, . . 

Of the Earth and the Moon, 

Of Mars, ..... 

Of the new Planets, Ceres, Pallas, Juno, and Vesta 
Of Jupiter and his Satellites, 

Of Saturn, his '‘'atellites and Ring, . 

Of the Georgium Sidus and its Satellites, 

On Comets, . - . . . 

Of the Elongations, of the interior Planets, 


124 

124 

126 

129 

131 

139 

141 

142 
147 
150 
152 
15.3 








CONTENTS, Xi 


Of the Stationary and Retrograde Appearances of the Exterior 

Planets, . . . . . . , 154 

Of the Fixed Stars, . . . . , 155 

Of Solar and Lunar EcHpses, .... 158 

General Observations on Eclipses, . . . 160 

‘Number of Eclipses in a Year, . ^ . 1€1 


PART III. 

.CHAP. I. PROBLEMS PERFORMED BY THE TERRESTRIAL GLOBE. 


Problem 1. To find the Latitude of any given place, 16S 

Problem 2. To find all those places which have the same Latitude 
as any given place, 164 

Problem 3, To find the Longitude of any place, 164 

Problem 4. To find all those places that have the same Longi¬ 
tude as a given place, 165 

Problem 5. To find the Latitude and Longitude of any place, 166 
Problem 6. To find any place on the globe haying the Latitude 
and Longitude of that place given, 166 

Problem 7. To find the dilFerence of Latitude between any two 

places, 16T 

Problem 8. To find the difference of Longitude between any 

two places 168 

Problem. 9. To find the Distance between any two places, 169 

Problem 10. A place being given on the Globe, to find all 
places which are situated at the same Distance from it as any 
given place, 173 

Problem 11. Given the Latitude of a place, and its distance 
from a given place, to find that place whereof the Latitude is 
given, , 173 

Problem 12. Given the Longitude of a place, and its distance 
from a given place, to find that place whereof the Longitude 
is given, 174 

Problem 13. To find how many miles make a Degree of Lon¬ 
gitude in any givea parallel of Latitude. 175 

Problem 14. To find the bearing of one place from another, 176 

Problem 15. To find the Angle of position between two places, 177 

Problem 16. To find the Antceci, Perioeci, and Antipodes of any 
place, 180 

Problem 17. To find at what rate per hour the inhabitants of 
any given place are carried from west to east, by the Revolu¬ 
tion of the Earth on its Axis, 181 

Problem 18. A particular place and ( he hour of the day at that 
place being given, to find what hour it is at any other place. 182 
Problem 19. A particular place and the hour of the day being 
given, to find all places on the Globe where it is then noon, 
or any other given hour, 183 

Problem 20. I’o find the Sun’s longitude (commonly called the 

Sun’s place in the ecliptic) and his declination, 185 

Problem 2l. Fo place the Globe in the same situation with res¬ 


pect to the Sun, as the Earth is at the £4uiuuxe8, at the Sum* 




Xii CONTENTS. 

, Page 

mer Solstice, and at the Winter Solstice, and thereby to show 
the comparative lengths of the longest and shortest days, 187 

Problem 2.:^. To place the Globe in the same situation with res¬ 
pect to the Polar L*tar in the heavens, as the earth is to the in¬ 
habitants of the Equator, Sic. viz. to illustrate the three posi¬ 
tions of the “phere, Right, Parallel, and Oblique, so as to 
show the comparative length of tlie longest and shortest days, 192 
Problem The month and day of the month being given, to 
find all places of the Earth where the Sun is vertical on that 
day ; those places w here the sun does not set, and those places 
where he does not rise on the given day, 197 

Problem 24. A place being given in the Torrid Zone, to find 
those two days of the year on which the Sun will be vertical 
rat that place. 199 

Problem 25. The month and day of the month being given at 
any place (not in the frigid Zones) to find what other day of the 
year is of the same length, 199 

Problem 26. The month, day, and hour of the day being given, 

to find where the Sun is vertical at that instant 200 

Problem 27. The month, day, and hour of the day at any place 
being given, to find all those places of the Earth where the Sun 
is rising, those places where the Sun is setting, those places 
that have noon, that particular place where the Sun is vertical, 
those places that have morning twilight, those places that 
have evening twilight, and those places that have midnight, 202 
Problem 28. To find the time of the Sun’s rising and setting, 

and the length of the day and night at any place, 204 

Problem 29. The length of the day at any place being gb en, 

' to find the Sun’s declination, and the day of the month, 206 

Problem SO. I'o find the length of the longest day at any place 

in the north frigid zone, 207 

Problem Si. No find the length of the longest night at any place 
in the north frigid zone, 209 

Problem S2. To find the number of days which the Sun rises 

and sets at any place in the north frigid zone, 210 

Problem S3. To find in what degree of north Latitude, on any 
day between the 21st of March and the 21st of June, or in 
what degree of south Latitude, on any day between the 2Sd 
of September and the 21st of December, the Sun begins to 
shine constantly without setting; and also in what Latitude 
in the opposite hemisphere he begins to be totally absent. 212 

Problem 34. Any number of days, not exceeding 182, being 
given, to find the parallel of north Latitude in which the Sun 
does not set for that time, 213 

Problem 35. To find the beginning, end, and duration of twilight 

at any place, on any given day, 214 

Problem 36. To find the beginning, end, and duration of con¬ 
stant day or twilight at any place, 216 

Problem S7. To find the duration of twilight at the north pole, 217 
Problem S8. To find in what climate any given place on the 

Globe is situated, 217 

Problem 89. To find the breadths of the several climates be¬ 
tween the Equator and the Polar Circles, 219 

Problem 40. 1 o find that part of the equation of Time which 

depends on the obliquity of the Ecliptic, 220 

Problem 41. To find the Sun tmeridian altitude at any time of 
the year at any given place, ’ 221 


CONTENTS. 


Xlll 


Page 

Problem 42. When it is midnight at any place in the temperate 
or torrid Zones, to find the Sun^s altitude at any place (on the 
same meridian) in the north feigid Zone, where the Sun does 
not descend below the horizon, 223 

Problem 43. To find the Sun’s amplitude at any place, 224 

Problem 44, To find the Sun’s azimuth and his altitude at any 

place, the day an<l hour being given, 225 

Problem 45, The latitude of the place, day of the month, and 
the bull’s altitude being given, to find the Sun’s azimuth and the 
hour ot tile day, 227 

Problem 46. Given the latitude of the place, and the day of the 

month, to find at what hour the Sun is due east or west, 228 

Problem 47. Given the Sun’s meridian altitude and the day of 

the month, to find the latitude of the place, 229 

Problem 48 'I'he length of the longest day at any place, not 
within the Polar Circles, being given, to find the Latitude of 
that place, 251 

Problem 49. The latitude of a place, and the day of the month 
being given, to find how' much the Sun’s declination must in¬ 
crease or decrease tow ards the elevated pole, to make the day 
an hour shorter or longer than the given day, 232 

Problem 50. To find the Sun’s right ascension, oblique ascen¬ 
sion, oblique descension, ascensional difference and time of 
rising and setting at any place, 234 

Problem 51. Given the day of the month, and the Sun’s ampli¬ 
tude, to find the latitude of the place of observation, 235 

Problem 52. Given two observed altitudes of the Sun, the time 
elapsed between them, and the sun’s declination, to find the 
latitude, 237 

Problem 53. The day and hour being given when a solar eclipse 
will happen, to find where it will be visible, 238 

Problem 54. The day and hour being given when a lunar e- 
clipse will happen, to find where it will be visible, 239 

Problem 55, To find the time of the year when the .Sun or Moon 
will be liable to be iMjlipsed, 246 

Problem 56. To explain the phenomenon of the harvest Moon, 257 
Problem 57. The day and hour of an eclipse of any one of the 
Satellites of Jupiter being given, to find upon the Globe all 
those places where it will be visible, 249 

Problem 58. To place the Terrestrial Globe in the sun-shine, 
so that it may represent the natural position of the Earth, 25t 

Problem 59. 1 he latitude of a place being given, to find the hour 
of the day at any time when the Sun shines, 253 

Problem 60. To find the Sun’s altitude, by placing the Globe in 

the sun-shine, 254 

Problem 61. To find the Sun’s declination, his place in the E- 
cliptic, and his Azimuth, by placing the Globe in the sun- 
shine, 255 

Problem 62. To draw a meridian line upon a horizontal plane, 

and to determine the four cardinal points of the horizon, 255 

Problem 63. To make a horizontal dial for any latitude, 257 

Problem 64. To make a vertical dial, facing the south, in north 
latitude, 260 


CHAP. II. PROBLEMS PERFORMED BY THE CELESTIAL GLOBE. 

Problem 65. To find the right ascensipn and declination of the 
Sun or a Star, 


264 


CONTENTS. 


stv 

Pag« 

Problem 66. To find the latitude and longitude of a Star, 265 

Problem 67. The right ascension and declination of a Mar, the 
Moon, a Planet, or of a Comet, bein^ given, to find its place 
on the Globe, *^266. 

Problem 68. The latitude and longitude of the Moon, a Star, 
or a Planet given to find its place on the Globe, 267 

Problem 69. The day and hour, and the latitude of a place be¬ 
ing given, to find what Stars are rising, setting, culminating, iec. 267 
Problem 70. The latitude of a place day of the mouth, and 
hour being given, to place the Globe in such a manner as to re¬ 
present the Heavens at that time, in or«ier to find the rela¬ 
tive situations and names of the Constellations and remarkable 
Stars’ 269 

Problem 71. To find when any Star, or Planet, will rise, come 

to the meridian, and set at any given place, 269 

Problem 72. To find the amplitude of any Star, rts oblique as¬ 
cension and descension, and its diurnal arc. for any given day, 271 
Problem 73. The latitude of a place given, to find the time of 
the year at which any known Star rises or sets acronycally, 
that is, when it rises or sets at sun-setting, 271 

Problem 74. The latitude of a place given, to find the time of 
the year at which any known Star rises or sets cosmically, that 
is, when it rises or sets at sun-rising, 273 

Problem 75. To find the time of the year when any given Star 
rises or sets heliacally, 274 

Problem 76. The latitude of a place and the day of the month 
being given, to find all those Stars that rise and set acronycal¬ 
ly, cosmically, and heliacally, 276 

Problem 77. To illustrate the precession of the Equinoxes, 277 

Problem 78. To find the distances of the Stars from each other 
in degrees, 279 

Problem 79. To find what stars lie in or near the Moon’s path, 
or what Stars the Moon can eclipse, or make a near approach to, 279 
Problem 80. Given the latitude of the place and the day of the 
naontb, to find what Planets will be above the horizon after 
sun-setting, 280 

Problem 8l. Given the latitude of the place, day of the month, 
and hour of the night or morning, to find what Planets will be 
visible,at that hour, 281 

Problem 82, The latitude of the place and day of the month giv¬ 
en, to find how long Venus rises before the Sun when she is a 
morning star, and how long she sets after the Sun when she 
is an evening Star, 282 

Problem 83. The latitude of a place and day of the month be¬ 
ing given, to find the meridian altitude of any Star or Planet, 284 
Problem 84. To find all those places on the Earth to which the 

Moon will be nearly vertical on any given day, 285 

Problem 85. Given the latitinle of a place, day of the month, 
and the altitude of a Star, to find the hour of the night, and the 
Star’s azimuth, ggg 

Problem 86 Given the latitude of a place, day of the month, 
and hour of the day, to find the altitude of any Star, and its 
azimuth, 287 

Problem 87. Given the latitude of a place, day of the month, 
and azimuth of a Star, to find the hour of the night and the 
Star’s sdtitude, 288 


CONTENTS. 


XV 


Page 


Problem 88. Two Stars being given, the one on the meridian, 
and the other on the east or west part of the horizon, to find 
the latitude of the place, 289 

Problem 89. The latitude of the place, the day of the month, 
and two Stars that have the same azimuth, being given, to find 
the hour of the night, 290 

Problem 90. Hie latitude of the place, the day of the month, ^ 
and two ktars that have the same altitude, being given, to find 
the hour of the night, 291 

Problem 91. The altitude of two stars, having the same azimuth, -.i 
and that azimuth being given, to find the latitude of the place, 392' 
Problem 92. The day of the month being given, and the hour t* 
when any known Star rises or sets, to find the latitude of the 
place, 29S 

Problem 93. To find on what day of the year any given Star 

pas‘«es the meridian at any given hour, 293 

Problem 94. The day of the month being given, to find at what o 
hour any given Star comes to the meridian, 295 

Problem 95 Given the azimuth of a known Star, the latitude, 
and the hour, to find the Star’s altitude and the day of the 
month. 295 

Problem 96. The altitude of two Stars being given, to find the ' 
latitude of the place, 296 

Problem 97. The meridian altitude of a known Star being giv¬ 
en at any place, to find the latitude, 296 

Problem 98 The latitude of a place, day of the month, and 
hour of the day being given, to find the nonagesimal degree of 
the ecliptic, its altitude and azimuth, and the medium cceli, 297 
Problem 99. The latitude of a place, day of the month, and the i-'• 
hour, together with the altitude and azimuth of a Star being 
given, to find the Star, 298 

Problem 100. To find the time of the moon’s Southing, or com- ‘‘ . 

ing to the meridian of any place, on any given day of the month, 299 
Problem 101. The day of the month, latitude of the place, and 1 

the time of high water at the full and change of the moon, be- n 

ing given, to find the time of high w ater on the given day, 301 

Problem 102. To describe the apparent path of any planet or of 

a Comet, amongst the fixed Stars, &c. 305 


PROBLEMS WHICH MAY BE PERFORMED BY EITHER GLOBE. 


Problem 20. - 

- 25. 

- 28. 

-29. 

- SO. 

- 31. 

- 32. 

- S3. 

- 34. 

- 35. 

- 36. 

- 37. 

-S8. 

- 39. 

-- 40 . 

-- 41. 


Page 







185 Problem 43. 





. 

199 

44. 





• 

204 

45. 





• 

206 

46. 






207 

47. 





. 

209 

-- 48. 






2i0 

49. 





. 

212 

-50. 





. 

213 

-51. 





- 

215 

-- 52. 





• 

216 

- 55. 





. 

21-1 

-56. 





- 

217 

59. 






2l9 

-60. 





. 

220 

61. 



4 


m 

22i 



Page 

- - 224 

- - 225 

- - 22T 

- - 228 
^ - 229 

- . 231 

- - 232 

- - 234 

- - 235 

- - 237 

- - 246 

- - 247 

- - 25S 

- - 254 

- - 255 











































XVI 


CONTENTS. 


PART IV. 


Page 

A promiscuous collection of examples exercising the prob¬ 
lems on the globes 308 to 319 

A collection of questions, with references to the pages 
where the answers will be found ; designed as an assist¬ 
ant to the tutor in the examination of the student, 319 to 342 

A table of the latitudes and longitudes of some of the prin¬ 
cipal places in the world, 343 to 353 


INDEX TO THE TABLES. 


t. A table of the climates, 16 

2. Tables of the constellations, with the number of stars 
in each constellation, and the names of the principal 

stars, 23, 24, & 25 

3. An alphabetical list of the constellations, with the 
right ascension and declination of the middle of each, 

for the ready finding of them on the globe, 26 &27 

4. A table of the velocity and pressure of the winds, 112 

5. A table of the satellites of Jupiter, 144 

6. A table of the configurations of the satellites of Jupiter, 146 

7. A table of the satellites of Saturn, 149 

8. A table of the number of geographical and English 

miles which make a degree in any given parallel of lati¬ 
tude, 172 

9. A table of the equation of time, dependent on the ob¬ 

liquity of the ecliptic, for every degree of the sun’s lon¬ 
gitude, 220 

10. A table of all the visible eclipses which will happen 

in the present century, 241 

11. A table for finding the Moon’s age, the time of new 

and full moon, &;c. 244 

12. A table of the hour arcs and angles for a horizontal 

dial, for the latitude of London, 259 

13. A table of the hour arcs and angles for a vertical dial, 

for the latitude of London, 262 

14. A table of the equation of time, to be placed on a 

sun-dial, 263 

15. A table of the time of high water at new and full 

Moon, at the principal places in the British Islands, 304 

16. A table of the latitudes and longitudes of some of the 

principal places in the world, 343 to 353 


Five, Copper-plates to he placed at the end of the Book, 


4 


NEW TREATISE 


ON THE 


USE OF THE GLOBES. 


PART 1. 

Containing, 1. Explanation of the Lines on the artificial Globes, 
including Geographical and Astronomical Definitions, &c. 2. The 
Properties of Matter and the Laws of Motion. S. I'he Figure 
and Magnitude of the Earth. 4. The Diurnal and Annual Motion 
of the earth. 5. The Origin of Springs and Rivers, and of the 
Saltness of the Sea. 6. The Flux and Reflux of the Tides. 7. The 
natural Changes of the Earth, caused by Mountains, Floods, Vol¬ 
canoes, and Earthquakes. 8. Hypotheses of the Antediluvian 
World, and the Cause of Noah’s Flood. 9. The Atmosphere, Air, 
Winds, and Hurricanes. 10. Vapours, Fogs and Mists, Clouds, 
Dew and Hoar Frost, Snow and Hail, Thunder and Lightning, 
Falling Stars, Ignis Fatuus, Aurora Borealis, and the Rainbow. 


CHAPTER I. 

r 

Explanation of the Lines on the Artificial Globes, in^ 
chiding Geographical and Astronomical Defini¬ 
tions ; with a few Geographical Theorems. 

1. THE Terrestrial globe is an artificial rep¬ 
resentation of the earth. On this globe the four quar¬ 
ters of the world, the different empires, kingdoms, and 
countries; the chief cities, seas, rivers, &c. are truly 
represented, according to their relative situation on the 
real globe of the earth. The diurnal motion of this 
globe is from west to east* 


3 


DEFINITIONS, &c. 


If 

2. The CELESTIAL GLOBE IS an artificial representa¬ 
tion of the heavens, on which the stars are laid down in 
their natural situations. The diurnal motion of this 
globe is from east to west, and represents the apparent 
diurnal motion of the sun, moon and stars. In using 
this globe, the student is supposed to be situated in the 
centre of it, and viewing the >siars in the concave surface. 

3. The AXIS OF the earth (See Plate I.* Fig. 
1. and II.) is an imaginary line passing through the 
centre of it, upon which it is supposed to turn, and a- 
bout which all the heavenly bodies appear to have a 
diurnal revolution. This line is represented by the 
wire which passes from north to south, through the 
middle of the artificial globe. 

4. The POLES OF THE EARTH are the two extrem¬ 
ities of the axis, where it is supposed to cut the sur¬ 
face of the earth ; one of which is called the north, or 
arctic pole ; the other the south, or antarctic pole. The 
celestial poles are two imaginary pointsf in the heavens, 
exactly above the terrestrial poles. 

5. The BRAZEN MERIDIAN 19 the clrclc in wliich the 
artifical globe turns, and is divided into 360 equal parts, 
called degrees. J In the upper semicircle of the brass 
meridian, these degrees are numbered from 0 to 90, 
from the equator towards the poles, and are used for 
finding the latitudes of places. On the lower semicir¬ 
cle of the brass meridian they are numbered from 0 to 
90, from the poles towards the equator, and are used in 
the elevation of the poles. 


* Figure I. represents the frame of the globe, with the horizon, brass 
meridian, and axis; Figure II. the globe itself, with the lines on its 
surface. 

t rhe pole-star, is a star of the second magnitude, near the north 
pole, in the end of the tail of the Little Bear. Its mean right ascen¬ 
sion, for the beginning of the year 1804, was 13'’ 14' 43", and its de¬ 
clination 88° 15' 44" north. 

:j: Every circle is supposed to be divided into 360 equal parts, called 
degrees, each degree into 60 equal parts called minutes, each mitmte 
into 60 equal parts called seconds, &c.: a degree is, therefore, only a 
relative idea, and not an absolute quantity, except when applied to a 
great circle of the earth, as to the equator, or a meridian, in which cases 
it is 60 geographical miles, or 69^ English miles. A degree of a great 
circle in the heavens is a space nearly equal to twice the apparent di¬ 
ameter of the sun; or to twice that of the moon when considerably 
elevated above the horizon. 




DEFINITIONS, &c. 3 

6. Great circles divide the globe into two equal 
parls, as the equaior, ecliptic, &c. 

7. Small circles divide the globe into iwounequat 
parts, as the tropics, polar circles, parallels of iatiiude, 
&c. 

8. Meridians, or Lines of Longitude, are semicir¬ 
cles^ extending from the north to the south pole, and 
cutting the equator at right angles. Every place upon 
the globe is supposed to have a meridian passing through 
it, though there be only 24 drawn upon the terrestrial 
globe; the deficiency is supplied by the brass meridi¬ 
an. When the sun comes to the meridian of any place 
(not within the polar circles,) it is noon, or mid-day, at 
that place. 

9. The EQUATOR is a great circle of the earth, equL 
distant from the poles, and divides the globe into two 
hemispheres, northern and southern. The latitudes of 
places are counted from the equator, northward and 
southward; and the longitudes of places are reckoned 
upon it eastward and westward. 

The equator, when referred to the heavens, is called 
the equinoctial, because when the sun appears in it, the 
days and nights are equal all over the world, viz. 12 
hours each. The declinations of the sun, stars, and 
planets, are counted from the equinoctial northward 
and southward ; and their right ascensions are reckon¬ 
ed upon it eastward round the celestial globe from 0 to 
360 degrees. 

10. The FIRST MERIDIAN is that from which geog¬ 
raphers begin to count the longitudes of places. In 
English maps and globes, the first meridian is a semicir¬ 
cle supposed to pass through London, or the royal ob¬ 
servatory at Greenwich. 

11. The ECLIPTIC is a great circle in which the suii 
makes his apparent annual progress among the fixed 
stars or it is the real path of the earth round the sun, 
and cuts the equinoctial in an angle of 23° 28'; the points 


* The sun’s apparent diurnal path is either in the equinoctial, or in 
lines nearly parallel to it; and his apparent annual path may be traced 
in the heavens, by observing what particular constellation in the zo¬ 
diac, is on the meridian at midnight; the opposite constellation will 
show, very nearly, the sun's place at noon on the same day. 



4 


DEFINITIONS, &c. 


of intersection are called the equinoctial points. The 
ecliptic is situated in the middle of the zodiac. 

12. The ZODIAC, on the celestial globe, is a space 
which extends about eight degrees on each side of the 
ecliptic, like a belt or girdle, within which the motions 
of all the planets are performed.* 

13. Signs of the zodiac. The ecliptic and zo¬ 
diac are divided into 12 equal parts, called signs, each 
containing 30 degrees. The sun makes his apparent 
annual progress through the ecliptic at the rate ot nearly 
a degree in a day. The names of the signs, and the 
days on which the sun enters them, are as follows; 

Spring Signs. | Smnmer Signs. 

V Aries, the Ram, 21st of 125 Cancer, the Crab, 21st 
March. | of June, 

y Taurus, the Bull, 19th I SI Leo, the Lion, 22d of 
of April. I July* 

n Gemini, the Twins, 20th | n Virgo, the Virgin, 22d 
of May. 5 of August. 

The six signs above are called northern signs, being 
north of the equinoctial; when the sun is in any ef 
these signs, his declination is north. 

Autumnal Signs^ ? Winter Signs. 

= 2 : Libra, the Balance, 23d | yS Capricornus, the Goat, 
of September. f 21st of December. 

Scorpio, the Scorpion, 5 CK* the Water- 

23d of October. I bearer, 20th January. 

t Sagittarius, the Arch-Jx Pisces, the Fishes, 19th 
er, 22d of November. ^ of February. 

The six latter signs are called southern signs ; when 
the sun is in any of these signs, his declination is south. 

The spring and autumnal signs are called ascending 
signs; because when the sun is in any of these signs, 
his declination is increasing. The summer and winter 
signs are called descending signs, because when the sun 
is in any of .these signs, his declination is decreasing. 

14. Declination of the sun, a star, or planet, is 
its distance from the equinoctial, northward or south- 


Except the new discovered planets, or Asteroids, Ceres and Pallas. 



DEFINITIONS, &c. 


5 


ward. When the sun is in the equinoctial he has no 
declination, and enlightens halt the globe from pole to 
pole. As he increases in north declination, he gradu¬ 
ally shines farther over the north pole, and leaves the 
south pole in darkness: in a similar manner, when he 
has south declination, he shines over the south pole, and 
leaves the north pole in darkness. The greatest decli¬ 
nation the sun can have, is 23° 28'; the greatest decli¬ 
nation a star can have, is 90°, and that of a planet, 30° 
28'* north or south. 

15. The TROPICS are two small circles, parallel to 
the equator (or equinoctial,) at the distance of 23° 28' 
from it; the northern is called the Tropic of Cancer, 
the southern is the 'Tropic of Capricorn. 'The tropics are 
the limits of the torrid zone, northward and southward. 

16. The POLAR CIRCLES are two small circles, par¬ 
allel to the equator (or equinoctial,) at the distance of 
66° 32' from it, or 23° 28' from each pole. The north¬ 
ern is called the arctic, the southern the antarctic circle. 

17. Parallels of latitude are small circles drawn 
through every ten degrees of latitude, on the terres¬ 
trial globe, parallel to the equator. Every place o» the 
globe is supposed to have a parallel of latitude drawn 
through it, though there be, generally, only sixteen par¬ 
allels of latitude drawn on the terrestrial globe. 

18. The HOUR CIRCLE on the artificial globes is a 
small circle of brass, with an index or pointer fixed to 
the north pole. The hour circle is divided into 24f 


* Except the planets, or Asteroids, Ceres and Pallas, which are 
nearly at the same distance from the sun ; the former, in April, 1802, 
W'as out of the zodiac, its latitude being 20® 4'15*' north. 

t Some globes have two rows of figures on the index, others but one. 
On Bardinas New British Globes, there is an hour circle at each pole, 
numbered with two ?*ovvs of figures. On Adams’ common globes there 
is but one index ; and on his improved globes the hours are counted by 
a brass wire with two indexes standing over the equator. The form 
of the circle is, however, a matter of little consequence, (provided it 
be placed under the brass meridian,) as the equator will answer every 
purpose to w'hich a circle of this kind can be applied, Mr. William 
Jones has made an hour circle to slide on the brass meridian of many 
of the globes fitted up by him : which is likewise meant to show the 
bearings of places; and Svime other instrument-makers have followed 
the same plan. An hour circle of this kind is nevertheless very incon¬ 
venient on account of the tr^’ub'e of removing it from the pole: more¬ 
over, in several problems where the sun’s declination is north, and less 
than about 12 degrees, this hour circle is useless. See Problem XXVII. 



6 


BEFIMTrONS, &c; 


equal parts, correspondent to the hours of the day; 
and these are again suodivided into halves and quar¬ 
ters. 

19. The HORIZON is a great circle which separates 
the visible half of the heavens from the invisible. This 
horizon, when applied to the earth, is distinguished by 
the sensible and rational horizon. 

20. The SENSIBLE, or visible horizon, is that which 
terminates our view, and is represented by that circle 
which we see in a clear day, where the earth, or sea, 
and the sky seem to meet * 

21. The RATIONAL, or true horizon, is an imaginary 
plane, passing through the centre of the earth, parallel 
to the sensible horizon. It determines the rising and 
setting of the sun, stars, and planets. 

22. The WOODEN horizon, circumscribing the arti¬ 
ficial globe, represents the rational horizon on the real 
globe. This horizon is divided into several concentric 
circles. On Bardinas New British Globes they are 
arranged in the following order : 

The first circle is marked amplitude, and is num¬ 
bered from the east towards the north and south, from 
0 to 90 degrees, and from the west towards the north 
and south in the same manner. 

The second circle is marked azimuth, and is num¬ 
bered from the north point of the horizon towards the 
east and west, from 0 to 90 degrees ; and from the south 
point of the horizon, towards the east and west in the 
same manner. 

The third circle contains the thirty-two points of the 
compass, divided into half and quarter points. The 
degrees in each point are to be found in the azimuth 
circle. 

The fourth circle contains the twelve signs of the 
zodiac, with the figure and character of each sign. 


* The sensible horizon extends only a few miles ; for example, if a 
man of 6 feet high were to stand on a large plane, or on the surface of 
the sea ; the utmost extent of his view, upon the earth or the sea, 
would be about three miles. Thus, if h be the height of the eye above 
th e surface of the sea, and d the diameter of the earth in feet, then 
X h, '^*11 show the distance which a person will be able to see, 
straight forward. KiitKh Trigonometry, second edition, Example, 
XLV. page T6. 


( 




DEFINITIONP, &c, .7 

The fifth circle contains the degrees of the signs, 
each sign comprehending 30 degrees. 

The sixth circle contains the days of the month, an¬ 
swering to each degree of the sun’s place in the ecliptic. 

The seventh circle contains the equation of time, or 
difference of time, shown by a well regulated clock and 
a correct sun-dial. When the clock ought to be faster 
than the dial, the number of minutes, expressing the 
difference, has the sign -f- before it; when the clock or 
w atch ought to be slower, the number of minutes in the 
difference has the sign — before it. This circle is pe¬ 
culiar to the JSew British Globes. 

The eighth circle contains the twelve calendar months 
of the year, &c. 

23. The CARDINAL POINTS of the horizon are east, 
west, north, and south. 

24. The CARDINAL POINTS in the heavens are the 
zenith, the nadir, and the points where the sun rises and 
sets. 

25. The CARDINAL POINTS of the ecliptic are the 
equinoctial and solstiiial points, which mark out the 
four seasons of the year ; and the cardinal signs are 
T Aries, 25 Cancer, ^ Libra, and VS Capricorn. 

26. The ZKNiTH is a point in the heavens exactly 
over our heads, and is the elevated pole of our horizon. 

27. The NADIR is a point in the heavens exactly un¬ 
der our feet, being the depressed pole of our horizon, 
and the zenilh, or elevated pole, of the horizon of our 
antipodes. 

28. The POLE of any circle is a point on the surface 
of the globe, 90 degrees distant from every part of that 
circle of which it is the pole. Thus, the poles of the 
world are 90 degrees from every part of the equator; 
the poles of the ecliptic (on the celestial globe) are 90 
degrees from every part of the ecliptic, and 23 degrees 
28 minutes from the poles of the equinoctial. Every 
circle on the globe, whether real or imaginary, has two 
poles diametrically opposite to each other. 

29. The EQUINOCTIAL POINTS are Aries and Libra, 
where the ecliptic cuts the equinoctial. The point 
Aries is called the vernal equinox, and the point Libra 
the autumnal equinox. When the sun is in either of 
these points, the days and nights on every part of the 
globe are equal to each other. 


DEFINITIONS, &c. 


30. The SOLSTITIAL POINTS are Cancer and Capri¬ 
corn. When the sun is in, or near, these points, the va¬ 
riation in his greatest altitude is scarcely peiceptible 
for several days; because the ecliptic near these points 
is almost parallel to the equinoctial, and therefore the 
sun has nearly the same declination for several days.— 
When the sun enters Cancer it is the longest day to all 
the inhabhants on the north side of the equator, and 
the shortest day to those on the south side. When 
the sun enters Capricorn it is the shortest day to those 
who live in north latitude, and the longest day to those 
who live in south latitude. 

31. A HEMISPHERE is half the surface of the globe; 
every great circle divides the globe into two hemis¬ 
pheres. The horizon divides the upper from the lower 
hemisphere in the heavens ; the equator separates the 
northern from the southern on the earth ; and the brass 
meridian, standing over any place on the terrestrial 
globe, divides the eastern from the western hemisphere. 

32. The mariner’s compass is a representation of 
the horizon, and is used by seamen to direct and ascer¬ 
tain the course of their ships. It consists of a circular 
brass box, which contains a paper card, divided into 32 
equal parts, and fixed on a magnetical needle that al¬ 
ways turns towards the north. Each point of the com¬ 
pass contains 11° 15', or 11^ degrees, being the 32d 
part of 360 degrees. 

33. The VARIATION of the compass is the devia'- 
tion of its points from the correspondent points in the 
heavens. When the north point of the compass is to 
the east of the true north point of the horizon, the va¬ 
riation is east; if it be to the west, the variation is west. 

The learner is to understand, that the compass does not always point 
directly north, but is subject to a small annual variation- A.t present, 
in England, the needle points about tk degrees to the westward of the 
north. 


AT LONDON IN 


B. M. S D. M. 

1576, the variation was, 11 15 E. | 1666, the variation was, 1 35 W, 

16B,. 6 10E.5 1683,. i SOW. 

16^2,. 6 OE. I irOO,.8 OW. 

1634,. 4 5E.J 1722,. U 

1657,. 0 P I 1747,. 17 40 W. 

I. 1780, - ^ . 23 41W, 









DEFINITIONS, 9 

The compass is used for setting the artiiicial globe north and south ; 
but care must be taken to make a proper allowance lor ihe variation. 

34. Latitude of a place, on the terrestrial globe, 
is its distance from the equator ; in degrees, minutes op 
geographical miles, &c. and is reckoned on the brass 
meridian, from the equator towards the north or south 
pole. 

35. Latitude of a star or planet, on the ce¬ 
lestial globe, is its distance from the ecliptic, northward 
or southward, counted towards the pole of the ecliptic, 
on the quadrant of altitude. The greatest latitude a 
star can have is 90 degrees, and the greatest latitude of 
a planet is nearly 8 degrees.* The sun being always in 
the ecliptic, has no latitude. 

36. The Quadrant of altitude, is a thin slip of 
brass divided upwards from 0 to 90 degrees, and down¬ 
wards from 0 to 18 degrees, and, when used, is general¬ 
ly screwed to the brass meridian. The upper divisions 
are used to determine the distances of places on the 
earth, the distances of the celestial bodies, their alti¬ 
tudes, &c. ; and the lower divisions are applied to find* 
ing the beginning, end, and duration of twilight. 

3r. Longitude of a place on the terrestrial globe, 
is the distance of the meridian of that place from the 
first meridian, reckoned in degrees and parts of a degree 
on the equator. Longitude is either eastward or west¬ 
ward, according as the place is eastward or westward 
of the first meridian. The greatest longitude that a 
place can have, is 180 degrees, or half the circumfer¬ 
ence of the globe. 

38. Longitude OF a star, or planet, is reckoned 
on the ecliptic from the point Aries, eastward, round the 
celestial globe. The longitude of the sun is what is 
called the sun’s place on the terrestrial globe. 

39. Almacanters, or parallels of altitude, 
are imaginary circles parallel to the horizon, and serve 
to show the height of the sun, moon, or stars. These 
circles are not drawn on the globe, but they may be de¬ 
scribed for any latitude by the quadrant of altitude. 


♦ The newly discovered planets, or Asteroids, Ceres and Pallas^ do 
not appear to be confined within this limit. 

4 



10 


DEFINITIONS, &c. 


40. Parallels of celestial latitude are small 
circles drawn on the celestial globe, parallel to the eclip¬ 
tic. 

41. Parallels of declination are small circles 
parallel to the equinoctial on the celestial globe, and are 
similar to the parallels of latitude, on the terrestrial 
globe. 

42. The Colures are two great circles passing through 
the poles of the world ; one of them passes through the 
equinoctial points, Aries and Libra ;* the other through 
the solstitial points, Cancer and Capricorn : hence, they 
are called the equinoctial and solstitial colures. They 
divide the ecliptic into four equal parts, and mark the 
four seasons of the year. 

43. Azimuth, or vertical circles, are imaginary 
great circles passing through the zenith and the nadir, 
cutting the horizon at right angles. The altitudes of 
the heavenly bodies are measured on these circles, 
which circles may be represented by screwing the quad¬ 
rant of altitude on the zenith of any place, and making 
the other end move along the wooden horizon of the 
globe. 

44. The prime vertical is that azimuth circle which 
passes through the east and west points of the horizon, 
and is always at right angles with the brass meridian, 
which may be considered as another vertical circle pas¬ 
sing through the north and south points of the horizon. 

45. The altitude of any object in the heavens, is 
an arch of a vertical circle, contained between the cen¬ 
tre of the object and the horizon. vVhen the object is 
upon the meridian, this arch is called the meridian alti¬ 
tude. 

46. The zenith distance of any celestial object, 
is the arch of a vertical circle contained between the 
centre of that object and the zenith ; or, it is what the 
altitude of the object wants of 90 degrees. When the 


* In the time of Hipparchus, the equinoctial colure is supposejl to 
have passed through the middle of the constellation Aries. Hippar¬ 
chus was a native of Nicaea, a town of Bythinia, in Asia Minor, about 
75 miles S. E. of Constantinople, now called Tnic; he made his obsei> 
vations between 160 and 135 years before Christ. ' ^ 



DEFINITIONS, &c. 11 

object is on the meridian, this arch is called the meridiao 
zenith distance. 

4T. The POLAR distance of any celestial object, 
is an arch of a meridian, contained between the centre 
of that object and the pole of the equinoctial. 

48. The AMPLITUDE of any object in the heavens, 
is an arch of the horizon, contained between the centre 
of the object when rising, or setting, and the east or 
west points of the horizon. Or, it is the distance which 
the sun ora star rises from the east, and sets from the 
west, and is used to find the variation of the compass at 
sea. In our summer, the sun rises to the north of the 
east, and sets to the north of the west : and in the win¬ 
ter, it rises to the south of the east, and sets to the south 
of the west. The sun never rises exactly in the east, 
nor sets exactly in the west, except at the time of the 
equinoxes. 

49. The AZIMUTH of any object in the heavens, is an 
arch of the horizon, contained between a vertical circle 
passing through the object, and the north or south points 
of the horizon. The azimuth of the sun, at any partic¬ 
ular hour, is used at sea for finding the variation of the 
compass. 

50. Hour circles, or horary circles, are the 
same as the meridians. They are drawn through every 
15 degrees* of the equator, each answering to an hour 5 
consequently, every degree of longitude answers to four 
minutes of time, every half degree to two minutes, and 
every quarter of a degree to one minute. 

On the globes these circles are supplied by the brass 
meridian, the hour circle, and its index. 

51. The SIX o’clock hour line. As the meridian 
of any place, with respect to the sun, is called the 12 - 
o’clock hour circle ; so that great circle passing through 
the poles which is 90 degrees distant from it on the 
equator, is called, by astronomers, the six o’clock hour 
circle, or the six o’clock hour line. The sun and stars 
are on the eastern half of this circle 6 hours before they 
come to the meridian ; and on the western half, six hours 
after they have passed the meridian. 


I* bn Cari/’s large Globe#, the meridian# are drawn through every 10 
degrees, as on a Map, 



12 


DEFINITIONS, &c. 


52. Culminating point of a star or planet, is that 
point of its orbit which, on any given day, is the most 
elevated. Hence, a star or planet is said to culminate 
when it comes to the meridian of any place ; for then 
its altitude at that place is the greatest. 

53. Apparent noon, is the time when the sun comes 
to the meridian; viz. 12 o’clock, as shown by a correct 
sun-dial. 

54. True or mean noon, 12 o’clock, as shown by 
a well regulated clock, adjusted to go 24 hours in a 
mean solar day, 

55. The EQ.UATION OF TIME at noon, is the interval 
between the true and apparent noon, viz. it is the dif¬ 
ference of time shown by a well regulated clock and a 
correct sun-dial. 

56. A TRUE SOLAR DAY is the time from the sun’s 
leaving the meridian of any place, on any day, till it re¬ 
turns to the same meridian on the next day ; viz. it is the 
time elapsed from 12 o’clock at noon, on any day, to 
12 o’clock at noon on the next day, as shown by a cor¬ 
rect sun-dial. A true solar day is subject to a continual 
variation, arising from the obliquity of the ecliptic, and 
the unequal motion of the earth in its orbit ; the dura¬ 
tion thereof sometimes exceeds, at others falls short, of 
24 hours, and the variation is the greatest about the first 
of November, when the solar day is 16’ 15" less than 
24 hours, as shown by a well regulated clock. 

57'. A MEAN SOLAR DAY is mcasurcd by equal mo¬ 
tion, as by a clock or time-piece, and consists of 24 hours. 
There are in the course of a year as many mean solar 
days as there are true solar days, the clock being as 
much faster than the sun-dial on some days of the year, 
as the sun-dial is faster than the clock on others. Thus 
the clock is faster than the sun-dial, from the 24th of 
December to the 15th of April, and froip the 16th of 
June to the 31st of August: but from the 15th of April 
to the 16th of June, and from the 31st of August to 
the 24th of December, the sun-dial is faster than the 
clock. When the clock is faster than the sun-dial, the 
true solar day exceeds 24 hours ; and when the sun-dial 
is faster than the clock, the true solar day is less than 
24 hours ; but when the clock and the sun-dial agree, 
viz. about the 15lh of April, 16th of Juno, 31st of Au- 


13 


DEFINITIONS, &c. 

gust, and 24th of December, the true solar day is exact¬ 
ly 24 hours. 

58. The ASTRONOMICAL DAY IS reckoned from noon 
to noon, and consists of 24 hours. This is called a na- 
tural day, being of I he same length in all latitudes. 

59. The ARTIFICIAL DAY, is the time elapsed be¬ 
tween the sun’s rising and setting, and is variable ac¬ 
cording to the different latitudes of places. 

60. The CIVIL day, like the astronomical or natural 
day consists of 24 hours, but begins differently in dif¬ 
ferent nations. The ancient Babylonians, Persians, 
Syrians, and most of the eastern nations, began their 
day at sun-rising. The ancient Athenians, the Jews, 
See. began their day at sun-setting, which custom is fol¬ 
lowed by the modern Austrians, Bohemians, Silesians, 
Italians, Chinese, &c. The Arabians begin their day 
at noon, like the modern astronomers. The ancient 
Egyptians, Romans, &c. began their day at midnight, 
and this method is followed by the English, French, 
Germans, Dutch, Spanish, and Portuguese. 

61. A siDERiAL DAY is the interval of time from the 
passage of any fixed star over the meridian, till it returns 
to it again : or, it is the time which the earth takes to 
revolve once round its axis, and consists of 23 hours, 
56 minutes, 4 seconds. 

In elementary books of Astronomy and the globes, the learner is 
generally told, that the earth turns on its axis from west to east in 24 
hours ; but the truth is, thart it turns on its axis in 23 hours, 56 min¬ 
utes, 4 seconds, making about 366 revolutions in 365 days, or a year. 
The natural day would always consist of 23 hours, 56 minutes, 4 sec¬ 
onds, instead of 24 hours, if the earth had no other motion than that on 
its axis; but while the earth has revolved eastward once round its ax¬ 
is, it has advanced nearly one degree* eastward in its orbit. To illus¬ 
trate this, suppose the sun to be upon any particular meridian at 12 
p^clock, on any day ; in the space of 23 hours, 56 minutes, 4 seconds 
afterwards, the earth will have performed one entire revolution; but it 
will at the same time have advanced nearly one degree eastward in its 
orbit, and consequently, that meridian which was opposite to the sun 
the day before, will be now one degree eastward of it; before the sun 
appears again on the same meridian; so that the time from the son’s 
being on the meridian on any day, to its appearance on the same meri¬ 
dian the next day, is 24 hours. 


* The earth goes round the sun in 365^ days nearly ; and the eclip¬ 
tic, which »s the earth’s path round the sun, consists of 360 degrees ; 
hence, by the rule of three, as 365^ D : 360 deg. ; • 1 D;59'8"2'", 
the daily mean motion of the earth in its orbit, or the apparent meaa 
motion of the sun in a day. 



14 


DEFINITIONS, &c. 


62. A SOLAR YEAR, or tropical year, is the time the 
sun takes in passing through the ecliptic, from one trop¬ 
ic, or equinox, till it returns to it again ; and consists of 
865 days, 5 hours, 48 rninutes, 48 seconds. 

68. A siDERiAL YEAR is the space of time which the 
sun takes in passing from any fixed star, till he returns 
to it again, and consists of 365 days, 6 hours, 9 minutes, 
12 seconds; the siderial year is therefore 20 minutes, 
24 seconds longer than the tropical year, and the sun 
returns to the equinox every year before he returns to 
the same point of the heavens ; consequently, the equi¬ 
noctial points have a retrograde motion. 

64. The PRECESsiopj of the equinoxes (or more 
properly, the recession of the equinoxes) is a slow mo¬ 
tion which the equinoctial points have from east to west, 
contrary to the order of the signs, which is from west 
to east. 

This motion, from the best observations, is about 50| 
seconds in a year, so that it would require 25,791 years* 
for the equinoctial points to perform an entire revolu¬ 
tion westward round the globe. 

In the time of Hipparchus, and the oldest astronomers, the equinoc¬ 
tial points were fixed in Aries and Libra: but the signs which v*ere 
then in conjunction with the sun. when he was in the equinox, are now 
a whole sign, or 30 decrees eastward of it; so that Aries is now in 
Taurus, Taurus in Gemini, &c. as may be seen on the celestial globe. 
Hence, also, the stars which rose and set at any particular season of the 
year in the times of Hesiod,t Eudoxus,f Pliny,$ &c. do not answer to 
the description given by these writers. 


* For the circumference of the equator is 360 degrees ; and as 50i"i 
1 year : : 360 deg.: “^5,791 years. 

t Hesiod was a celebrated Grecian poet, born at Ascra, in Boeotia, 
supposed to have flourished in the time of Homer: he was the first who 
wrote a poem on Agriculture, entitled The Works and the Days, in 
which he introduces the rising and setting of particular stars, &:c. Sev¬ 
eral editions of his works are now extant. 

I Eudoxus was a great geometrician and astronomer, from whom 
Euclid the geometrician is said to have borrowed great part of his ele¬ 
ments of geometry. Eudoxus was born at Cnidus, a town of Caria, in 
Asia Minor ; he flourished about 370 years before Christ- 

} Pliny, generally catled Pliny the Elder, was born at Verona, in 
Italy; he composed a work on natural history, in 37 books ; it treats of 
the stars, the heavens, wind, rain, hail, minerals, trees, flowers, plants, 
birds, fishes and beasts ; besides a geographical description of every 
place on the globe, Ac. Ac. Pliny perished by an eruption of Vesuvius, 
in the 79th year of Christ, from too eager a curiosity in observing the 
phenomenon. 



DEFINITIONS, &c. 15 

65. Positions OF the sphere are three; right, 
parallel, and oblique. 

6t>. 4 RIGHT SPHERE is that positiou of the earth 
where the equator passes through the zenith and the 
nadir, the poles being in the rational horizon. The in¬ 
habitants who have this position of the sphere live at 
the equator ; it is called a right sphere because all the 
parallels of latitude cut the horizon ai right angles, and 
the horizon divides them into two equal parts, making 
equal daj and night. 

67. A PARALLEL SPHERE, is that position the earth 
has when the rational horizon coincides with the equa¬ 
tor, the poles being in the zenith and nadir. The in¬ 
habitants who have this position of the sphere (if there 
be any such inhabitants) live at the pole ; it is called 
a parallel sphere, because all the parallels of latitude 
are parallel to the horizon, and the sun appears above 
the horizon for six months together. 

68. An OBL1Q.UE SPHERE is that position the earth 
has when the rational horizon cuts the equator obliquely, 
and hence it derives its name. All inhabitants on the 
face of the earth (except those who live exactly at the 
poles of the equator) have this position of the sphere, 
and the days and nights are of unequal lengths, the 
parallels of latitude being divided into unequal parts by 
the rational horizon. 

69. Climate is a part of the surface of the earth con¬ 
tained between two small circles parallel to the equator, 
and of such a breadth, that the longest day in the paral¬ 
lel nearest the pole, exceeds the longest day in the par¬ 
allel of latitude next the equator, by half an hour, in 
the torrid and temperate zones, or by a month in the 
frigid zones ; so that there are 24 climates between the 
equator and each polar circle, and six climates between 
each polar circle and its pole. 

From ttie above definition it appears, that all places situated on the 
same parallel of latitude are in the same climate ; but we must not infer 
from thence, that they have the same atmospherical temperature ; 
large tracts of uncultivated lands, sandy deserts, elevated situations, 
woods, morasses, lakes, &;c. have a considerable effect on the atmos¬ 
phere For instance, in Canada, in about the latitude of Paris, and the 
south of England, the cold is so excessive, that the greatest rivers are 
froz-^n over from December to April and the snow commonly lies from 
four to six feet deep. The Andes mountains, though part of them are 


16 


DEFINITIONS, 


situated in the torrid zone, are at the summit covered with snow, which 
cools the air in the adjacent country. The heal on the wftjstern coast 
of Africa, after the wind has passed over the sandy desert, is almost 
suffocating; whilst that same wind having passed over the Atlantic 
Ocean, is cool and pleasant to the inhabitants of the Caribbean Islands. 

—---—■——J 


I. Climates between the Equator and the Polar Circles. 


Climate. 

Ends in 
Lati- 
tude. 

Where 

the 

longest 
Day IS. 

'Breadths \ 
j of the ; 
\Climates. \ 

1 i 

\ 2 

Ends in 
Lali~ 
lude. 

Where 

the 

longest 
Day is. 

Breadths 
of the 
climates. 


1). 

JM. 

H, 

M. 

D, 

M. j 


D. 

M. 

H. 

M. 

D. M. 

I 

8 

34 

12 

SO 

8 

34 ; 

i XIII 

59 

59 

18 

30 

1 32 

11 

16 

44 

13 

— 

8 

10 ; 

1 XIV 

61 

18 

19 

— 

1 19 

III 

24 

12 

13 

SO 

7 

28 \ 

\ XV 

62 

26 

19 

SO 

1 8 

IV 

30 

48 

14 

— 

6 

S6; 

^ XVI 

63 

22 

20 

—- 

— 56 

V 

36 

SI 

14 

so 

5 

43 \ 

! XVll 

64 

10 

20 

so 

— 48 

VI 

41 

24 

15 

— 

4 

53 \ 

; xvm 

64 

50 

21 

— 

— 40 

VII 

45 

32 

15 

so 

4 

8 \ 

; XIX 

65 

22 

21 

so 

— 32 

VIII 

49 

2 

16 


S 

30 \ 

: XX 

65 

48 

22 

— 

— 26' 

IX 

51 

59 

16 

so 

2 

57 j 

; XXI 

66 

5 

22 

so 

— 17 

X 

54 

SO 

17 

— 

2 

31 

XXII 

66 

21 

23 

— 

— 16 

XI 

56 

S8 

17 

so 

2 

8 

XXIll 

66 

29 

23 

so 

— 8 

XII 

58 

27 

18 

— 

1 

49 \ 

XXIV 

66 

32 

24 

— 

— ' 3 


WVVWWXA/WWVV^WVVWVWVWWV -.^^vwvwvvvvv^vwvvwv^vwvw 


II. Climates between the Polar Circles and the Poles. 


Climate, 

Ends 

in Lat¬ 
itude. 

Where 

the 

longest 
Day is. 

Breadths i g: 

of the 1 g 

climates. | ^ 

Ends 
in Lat¬ 
itude. 

Where 

the 

longest 
Day is 

Brendihs 
of the 
cimates 


D. M. 

DaysM 

D. M. \ 

D. M. 

DaysM 

L). M. 

XXV 

67 18 

30 or 1 

— 46^XXVI1I 

77 40 

120or4 

4 35 

XXVI 

69 33 

60 — 2 

2 15 \ XXTX 

82 59 

150—5 

5 19 

XXVII173 5 

90 —S 

S Si \ XXX 

90 — 

180—6 

7 1 




The preceding tables may be constructed by the globes, as will be 
shown in the problems, but not with that exactness given above. Ta- 
hies of this kind are generally copied from one author into another, 
without any explanation of the principles on which they are founded. 





























DEFINITIONS, &c. 
Construction of the first Table. 


17 


In plate IV. figure IV.^ HO represents the horizon, the equator, 
c a[o ^ parallel of the sun’s greatest declination, NO the elevation 
of the pole or latitude of the place ; the angle c a 6, measured by the 
arch 0,0, the complement of the latitude ; a 5 is the ascensional dilfer- 
ence, or the time the sun rises before 6 o’clock, and 6 c the sun’s decli¬ 
nation. Hence, by Baron Napier’s rules (see Keith’s Spherical T rigo- 
nometry) rad. X sine a b =: cotangent a* (or tangent N O) X tangent 
be, 

viz. Tangent of the sun’s greatest declination 23® 28', 

Is to radius, sine of 90 degrees ; 

As sine of the sun’s aseensional difference^ 

Is to the tangent of the latitude. 

A general rule : 


At the end of the first climate, the sun rises i before 6 ; and in every 
climate, if you take half the length of the longest day, and deducts 
hours therefrom, the remainder turned into degrees will give the ascen¬ 
sional difference. Hence the ascensional difference, for the first climate, 
is 1.1 minutes of time, equal to 3° 45'; for the second climate SO min- 
utes=T® SO'; for the third climate 45 minutes=ll® 15'; for the fourth 
climate 1 liour=l5®. &c. 

Tangent of 2S® 28' - 9.6S761 $ Tangent of 2S® 28' - 9.6S761 

Is to radius, sine of 90® 10.00000 | Is to radius sine, of 90® 10.00000 

Assine ofS® 45' - - 8.81560 ^ As sine of T® 30' - 9.11.570 


Is to tang. lat. 8® 34' 9.17799 


Is to tang, lat 16® 44' 


9.47809 


Construction of the second Table, 

The longest day is the 21st of June, when the sun’s declination is 
23® 28' north. Count half the length of the day from the 21st of June 
forward and backward ; find the sun’s declination answering to those 
two days in the nautical almanac, or in a table of the sun’s declina¬ 
tion i add the two declinations together, and divide their sum by 2, 
subtract the quotient from 90 degrees, and the remainder is the latitude. 
As the sun’s declination is variable, it ought to be taken out of the al¬ 
manac, or tables, for leap year and the three following years; a mean 
of the.se declinations used as above will give the latitude as correct as 
the nature of the problem admits of, and in this manner the second table 
was constructed—Riccioli (an Italian astronomer and raatbematieian, 
born at Ferrara, in the Pope’s dominions, 1598,) in hi.s Asironomia 
Rfformata, published in 1665^ makes an allowance for the refraction of 
the atmosphere in a table of climates. He considers the increase of 
days to be by half hours, from 12 to 16 hours ; by hours, from 16 to 20 
hours; by 2 hours from 20 to 24 hours, and by months in the frigid 
zones, making the number of the days of each month in the north frigid 
zone something more than those in the south; but, as the refraction 
of the atmosphere is so extremely vaiiable that scarcely any tw’o math- 
ematiciano agree with respect to the quantity, it is evident that a table 
of climates, calculated with such an uncertain allowance, can be of no 
material advantage. 




18 


DEFINITIONS, &c. 


fO. A ZONE is a portion of the surface of the earth 
Contained between two stnall circles parallel to the 
equator, and is similar to the term climate, for pointing 
out the situations of places on the earth, but less exact ; 
as there are only Jive zortes, whereas there are 60cli- 
ttiates. 

71. I'he TORRID ZONE extends from the tropic of 
Cancer to the tropic of Capricorn, and is 46° 56^ broad. 
This zone was thought by the ancients to be uninhabi¬ 
ted, because it is continually exposed to the direct rays 
of the sun ; and such parts of the torrid zone as were 
known to them were sandy deserts, as the middle of Af¬ 
rica, Arabia, &c. : and this sandy desert extends be¬ 
yond the left bank of the Indus, toward Agimere. But 
these deserts are not produced merely by the excessive 
heat of the sun, as the ancients imagined; because it is 
well known, that moisture is one of the greatest incon¬ 
veniences in several parts of the torrid zone. 

72. The TWO temperate zones. The north tem¬ 
perate zone extends from the tropic of Cancer to the 
arctic circle; and the south temperate zone from the 
tropic of Capricorn to the antarctic circle. These zones 
are each 43° 4' broad, and were called temperate by the 
ancients, because meeting the sun’s rays obliquely, they 
enjoy a moderate degree of heat. 

73. The TWO frigid zones. The north frigid zone, 
or rather segment of the sphere, is bounded by the arctic 
circle. The north pole, which is 23° 28' from the arctic 
circle, is situated in the centre of this zone. The south 
frigid zone is bounded by the antarctic circle, distant 
23° 28' from the south pole, which is situated in the 
centre of this zone. 

74. Amphiscii are the inhabitants of the torrid zone; 
so called because they cast their shadows both north and 
south at different times of the year; the sun being some¬ 
times to the south of them at noon, and at other times to 
the north. When the sun is vertical, or in the zenith, 
which happens twice in the year, the inhabitants have 
no shadow, and are then called Ascii, or shadowless. 

75. Heteroscii is a name given to the inhabitants of 
the temperate zones, because they cast their shadows at 
noon only one way. Thus the shadow of'an inhabitant 
of the north temperate zone always falls to the north at 


DEFINITIONS, &c. 


19 


noon, because the sun is then directly south ; and an 
inhabitant of the south temperate zone casts his shadow 
towards the south at noon, because the sun is due north 
at that time. 

76. Periscii are those people who inhabit the frigid 
zones, so called, because their shadows, during a revo¬ 
lution of the earth on its axis, are directed towards every 
point of the compass. In the frigid zones the sun does 
not set during several revolutions of the earth on its axis. 

77. Antoeci are those who live in the same degree 
of longitude, and in equal degrees of latitude, but the one 
has north and the other south latitude. They have 
noon at the same lime, but contrary seasons of the year; 
consequently, the length of the days to the one, is e- 
qual to the lengths of the nights to the other. Those 
who live at the equator have no Antoeci. 

78. Perioeci are those who live in the same latitude, 
but in oposite longitudes ; when it is noon with the one, 
it is midnight with the other ; they have the same length 
of days, and the same seasons of the year. The inhab¬ 
itants of the poles have no Perioeci. 

79. Antipodes are those inhabitants of the earth who 
live diametrically opposite to each other, and conse¬ 
quently walk feet to feet ; their latitudes, longitudes, 
seasons of the year, days, and nights, are all contrary to 
each other. 

80. The RIGHT ASCENSION of the sun, or a star, is 
that degree of the equinoctial, which rises with the sun, 
or a star, in a right sphere, and is reckoned from the 
equinoctial point Aries eastward round the globe. 

81. Oblicioe ASSENSION of the sun, or a star, is that 
degree of the equinoctial which sets with the sun or a 
star, in an oblique sphere, and is likewise counted froni 
tfie point Aries round the globe. 

^^82. Oblique descension of the sun or a star, is that 
degree of the equinoctial which sets with the sun or a 
star, in an oblique sphere. 

83. The Ascensional or descbnsional differ¬ 
ence, is the difference between the right and oblique 
ascension, or the difference between the right and oblique 
descension, and with respect to the sun, it is the time 
he rises before 6 in the summer, or se^s before 6 in the 
wintero 


20 


DEFINITIONS, 


84. The CREPUscuLifM, or twilight, is that faint 
light which we perceive before the sun rises, and after 
he sets. It is occasioned by the earth’s atmosphere 
refracting the rays of light, and reflecting them from the 
particles thereof. The twilight is supposed to end in 
the evening, when the sun is 18 degrees below the hori- 
zon, or when stars of the sixth magnitude (the smallest 
that are visible to the naked eye) begin to appear ; and 
the twilight is said to begin in the morning, or it is day~ 
break, when the sun is again within 18 degrees of the 
horizon. The twilight is the shortest at the equator, 
and longest at the poles; here the sun is near two months 
before he retreats 18 degrees below the horizon, or to 
the point where his rays are first admitted into the at¬ 
mosphere ; and he is only two months before he arrives 
at the sa ne parallel of latitude. 

85. Refraction. The earth is surrounded by a 
body of air, called the atmosphere, through which the 
rays of light come to the eye from all the heavenly bod¬ 
ies : and since these rays are emitted through a vacuum, 
or at least through a very rare medmm,^ and fall ob¬ 
liquely upon the atmosphere, which is a dense medium, 
they will, by the laws of optics, be refracted in tines ap¬ 
proaching nearer to a perpendicular from the place of the 
observer (or nearer to the zenith) than they would be, 
were the medium to be removed. Hence all the heaven¬ 
ly bodies appear higher than they really are, and the 
nearer they are to the horizon the greater the refraction, 
or difference between their apparent and true altitudes 
will be ; at noon the refraction is the least. The sun 
and the moon appear of an oval figure sometimes near 
the horizon, by reason of refraction ; for the under side 
being more refracted than the upper, the perpendicular 
diameter will be less than the horizontal one, which is 
not affected by refraction. 

Refraction is variable according to the different dens¬ 
ity of the air : hence it happens, that we sometimes arc 


♦ Any fluid, or substance, through which a ray of light can penetrate, 
is called a medium, as air, water, oil, glass, &c. the air near the sur¬ 
face of the earth is more dense than in the higher regions;,of the atmos¬ 
phere : and beyond the atmosphere, the^ rays of light are supposed to 
sneet with little or no resistance. 



DEFINITIONS, &c. 


21 


able to see the tops ot mountains, towers, or spires of 
churches, which at other times are invisible, though we 
stand in the same place. The ancients knew nothing of 
refraction: the first who composed a table thereof was 
Tycho Brahe* 

The sun’s meridian altitude on the longest day de¬ 
creases from the tropic of Cancer to the north pole ; and 
in the torrid zone, when the sun is vertical there is no re¬ 
fraction ; hence the refraction is the least in the torrid 
zone, and greatest at the poles. Varenius, in his geog¬ 
raphy, speaking of the wintering of the Dutch in Nova 
Zembla, latitude 76° north, in the year 1596, says they 
saw the sun in the year 1597 six days sooner than they 
would have seen him, had there been no refraction. 

86. Angle of position between two places on the 
terrestrial globe, is an angle at the zenith of one of the 
places; formed by the meridian of that place, and a ver¬ 
tical circle passing through the other place, being mea¬ 
sured on the horizon from the elevated pole towards the 
vertical circle. 

87. Rhumbs are the divisions of the horizon into 32 
parts, called the points of the compass. The ancients* 
were acquainted only with the four cardinal points, and 
the wind was said to blow from that point to which it 
was nearest. 

A Rhumb line, geometrically speaking, is a loxodromic 
or spiral curve, drawn or supposed to be drawn upon the 
earth, so as to cut each meridian at the same angle, call¬ 
ed the proper angle of the rhumb. If this line be con¬ 
tinued, it will never return into itself so as to form a cir¬ 
cle, except it happens to be due east and west, or due 
north and south; and it can never be a straight line up¬ 
on any map, except the meridians be parallel to each 
other, as in Mercator’s and the plane chart. Hence 
the diflSculty of finding the true bearing between two 
places on the terrestrial globe, or on any map but those 
above mentioned. The bearing found by a quadrant of 
altitude on a globe, is only the measure of a spherical 
angle upon the surface of that globe, as defined by the 
angle of position, and not the real bearing or rhumb, as 


* Pliny^s Nat. Hist. Lib, II. chap. 47. 



22 


DEFINITIONS, &c. 


shown by the compass, for, by the compass, if a place 
A bear due east from a place B, 1’^e place B will bear 
due west from the place A; but this is not the case 
when measured with a quadrant of altitude. 

88. The FIXED stars are so called, because they - 
have been usually observed to keep the same distance 
with respect to each other. The stars have an appa¬ 
rent motion from east to west, in circles parallel to the 
equinoctial, arising from the revolution of the earth on 
its axis, from west to east; and, on account of the pre¬ 
cession of the equinoxes, their longitudes increase a- 
bnit 501 seconds in a year ; this likewise causes a varia¬ 
tion in their declinations and right ascensions : their 
latitudes are also subject to a small variation. 

89. The POETICAL rising and setting of the 
STARS, so called because they are taken notice of by the 
ancient poets, who referred the rising and setting of the 
stars to the sun. Thus when a star rose with the sun, 
or set when the sun rose, it was said to rise and set 
Cosmically, When a star rose at sun-setting, or set 
with the sun, it was said to rise and set Achronically, 
When a star first became visible in the morning, after 
having been so near the sun as to be hid by the splen¬ 
dour of his rays, it was said to rise Heliacnlly ; and 
when a star first became invisible in the evening, on ac¬ 
count of its nearness to the sun, it was said to set Heli~ 
acally, 

90. A CONSTELLATION is an assemblage of stars on 
the surface of the celestial globe, circumscribed by the 
outlines of some assumed figure, as a ram, a dragon, a 
hear, &c. This division of the stars into constellations 
is necessary, in order to direct a person to any part of 
the heavens where a particular star is situated. 

The following Tables contain all the constellations on the New Brit^ 
ish Globes. 

The zodiacal constellations are 12 in number, the northern constella¬ 
tions 34, and the southern 47, making in the whole 93. 

Foreign mathematicians have changed the names of some of these 
constellations, diminished the number of stars in others, in order to 
form new constellations, &c. but as these modern improvements havie 
not been introduced upon our globes, it will be unnecessary to specify 
them here. 

The largest stars are called stars of the first magnitude; those of the 
sixth magnitude are the smallest that can be seen by the naked eye. 
The number of stars in each constellation, except those marked with 
asterisks, are taken from Flamstead. 


DEFINITIONS, 


23 


I. CONSTELLATIONS IN THE ZODIAC. 

CONSTELLATIONS. 

ISum- 

Names of the principal 

ber of 

Stars, and their magni¬ 


Stars. 

tudes. 

1. Aries, The Ram^ 

66 

Arietis, 2. 



C iVldebaran, 1. 

2. Taurus, The Bull^ 

141 

The Pleiades. 

C Hie Hyades. 

Gemini, The Ticins^ 

i 

85 

Castor and Pollux, 1. 2. 

4. Cancer, The Crab^ 

5. Leo, The Lion^ 

83 

^ Regulus, or Lion’s 

95 

^ Heart, 1. 

6. Virgo, The Virgin^ - 

110 

( Spica Virginis, 1, 

^ Vendemiatrix, 2. 

7. Libra, The Balance^ 

51 


8. Scorpio, The Scorpion, 

44 

Antares, 1. 

9. Sagittarius, The Archer, 

69 

10. Capricornus, The Goat, 

51 


11. Aquarius, The Water-bearer, 

108 

Scheat, 3. 

12. Pisces, The Fishes, 

113 


II. THE NORTHERN CONSTELLATIONS. 


Num¬ 

Names of the principal , 

CONSTELLATIONS. 

ber of 

Stars, and their Mag¬ 


Stars. 

nitudes. 

1. Mons IVlaenalufi, The mountain 



Mcenalus, - - - 

11 


2. Serpens, The Serpent, 

64 


S. Serpen tarius The Serpent-hearer, 
4. ^Taurus Poniatowski, Bull of 

74 

Ras Alhagus, 2i 

Poniatowski, 

7 


5. Sobieski^sShield, 

8 

' 

g > Aquila, I'he Eagle, ) 
r'^Vntinbns, ^ 

71 

Altair, 1. ’ 

7. Equulus, The little Horse, 

10 


8. Leo Minor, The little Lion, 

53 

Deneb, 2. I 

9. Coma Berenices, Beremce’s/iair, 

43 

{Aslerion et Chara, vel, 


1 

10. < Canes Venatici, The Grey- C 

25 

I 

f “ hounds. 3 



11. Bootes, - _ - 

54 

Arcturus. 1. Mirach, 3, 

12. Corona Borealis, The northern 



Crown, - - - 

21 

Alphacca,2. 

(Hercules - - 

IS. < Cerberus, 7'/ie </ire€-^carferf^ 
f Dog, - - - 3 

113 

Ras Algetki 3 in the head 
of Hercules. , 

14. Lvra, The Harp, 

15. Vulpecula et Anser, The Fox 

21 

Vega, 1. 

and Goose, 

35 


'16. Sagitta, i'/ie Arrow, 

18 

• 

















24 


DEFINITIONS, kc. 



:\urn- 

Names of the principal 

NOR rH»N. CONSTELLATIONS. 

ber of 

Stars, and their Mag¬ 


Stars. 

nitudes. 

ir. Ddphinus, The Dolphin, 

18, Pegasus, The Flying Horse, 

18 


89 

Markab. 2. Scheat, 2. 

19. Andromeda, - - - 

66 

Mirach, 2. Alraaach,2. 

to. Triangulura, The Triangle, 

21. Triangulum Minus, The Little Tri- 

11 


angle, - - - - 

5 


22. * Musca, T/ie F/j/, 

6 


The following northern constellations do 
not set in the latitude of London. 

um¬ 
ber of 
Stars. 

Names of the principal 
Stars, and their Mag¬ 
nitudes. 

23. Ursa Minor, The little Bear, 

24 

Pole Star, 2. 

24. Ursa Major, The great Bear, 

87 

Dubhe,2. Aliotb, 2. 
Benetnach, 2 . 

25. *Cor Caroli, Charleses Heart, 

3 


26. Drnco, The Dragon, 

80 

Rastaben, 2. 

27. Cygnus, The Swan, 

81 

Deneb Adige, 1. 

28. Lacerta, The Lizard, 

16 

29. Cepheus, - . - - 

35 

Alderamin, 3. 

30. Cassiopeia, - - - - 

55 

Schedar, 3. 

C Perseus, - - - - 

31. < Caput Medusee, Head of Me- V 
C dusa, - - - "3 

59 

5 Algenib, 2. 

1 Algol, 2. 

32. Cameleopardalus, TheCameleopard, 

58 

Capella, 1. 

S3. Auriga. The Charioteer or Wagoner, 

66 

34. Lynx, The Lynx, - - 1 

44 1 

VWVWVWVWVWWX/VWWX/VWVWVWWVVWWVVWVWVWVWVWWVVW 

III. THE SOUTHERN CONSTELLA TIONS. 


Num¬ 

Names of the p rincipal 

CONSTELLATIONS. 

ber of 

Stars and their .Mag¬ 


Stars. 

nitudes. 

1. Cetus, The Whale, 

97 

Menkur, 2 . 

2 . Eridanus, The river Po, 

84 

Archerner, 1. 

*3. Orion, - - . - 

78 

t Bellatrix, 2 . Betel- 
1 gues, 1 . Rigel, 1 . 

,4. Monoceros, The Unicorn, 

31 

j5. Canis Minor, The little Dog, - 

14 

Procyon, 1. 

ie. Hydra, . - - . 

Sextans, The Sextant, 

60 

Cor Hydrae, 1. 

41 

[8. *Microscopium, The Microscope, 

|9. Piscis Notius vel Australis, The 

10 


southern Fish, ... 

24 

Fomalhaut, 1. 

10. *Officina Sculptoria, The SculptoPs 

12 

Shop, - . - . 


11. *Fornax Chemica, The Furnace, 

12 . *Brandenburgium Sceptrum, The 

14 


Sceptre of Brandenburgh, 

3 


IS. Lepus, The Hare, 

19 


14. *Columba Noachi, Noah^s Dove, 

10 

. 














DEFINITIONS, &c. 


25 


SOUTHERN CONSTELLATIONS. 

Num 

ber of 
Stars 

Names of the principal 

Stars, and their 
Magnitudes* 

15. Canis Major, The great Dog, 

16. *Pyxis Nautica, The Mariner’^s 

Compass, *• ’ " “. 

17. * Machina Pneumatica, The Air 

Pump, - - - - 

18. Crater, The Cup or Goblet, 

19. Corvus, The Crow, 

31 

4 

3 

31 

9 

Sirius, 1. 

Alices, 3. 

Algorab, 3. 

The following southern constellations do 
not rise in the latitude of London* 

Num¬ 
ber of 
Stars. 

Names of the princi¬ 
pal Stars, and their 
Magnitudes. 

2(>. Centaurus, The Centaur, 

35 


21 . Lupus, The Wolf, 

24 


22. * Norma, vel Kuadra Euclidis, Eu¬ 
clid's Square, _ - - 

12 


23. ^Circinus. T/ie Cowijjftsses, 

4 


2A. ^Triangulum Australe, The southern 
Triangle, - - - 

5 


25 *Cruyi, The Cross, 

5 


26. *Musca Australis, vel Apis, The 
southf'm Fly, or Bee, 

4 


27. *ChamcBleon, The Cameleon, - 

10 


28. Ara, The Altar, 

9 


29. *TeIescopium, The Telescope, 

9 


30. Corona Australis, The souihern 
Crown, - - - - 

12 


31. *lndus, The Indian, 

32. *Grus, The Crane, 

12 


13 


33. *Pavo, The Peacock, 

14 


34. *^Apus, vel Avis Indica, The Bird 
of Paradise, . - - 

11 


35. *Octans Hadleianus, Hadley^s Oc¬ 
tant, . - - - 

43 


36. *Phcenix, - - - - 

13 


37. ^Horologium, The Clock, 

12 


38. *Reticulus Rhomboidalis, TheRhom- 
boidal Net, - - - 

10 


39. *Hydrus, The Water-snake, 

10 


40. * Touchan, 77ie American Goose, 

9 


41. Mons Mensae, The Table Mountain, 

30 


42. ^Praxiteles, vei Cela Sculptoria, T/ie 
Graver's or Engraver's Tools, 

16 


43. *Equuleu 8 Pictorius, The Painter's 
Easel, - - . 

8 


44. ^Dorado, or Xiphias, The Sword 
Fish, - . - 

6 


45. Arga Navis, The Ship Argo, 

64 

Canopus, 1. 

1 

1 

46, *Piscis Volans, The Flying Fish, 

8 i 

47. •Kobur Caroli, Charles's Oak, 

12 ^ 


G 
















DEFINITIONS, &c. 


2(> 

Aji Alphabetical List of the Constellations with the 
Right Ascension {R.) and Declination (D.) of the 
middle of each, for the ready finding them on the 
Globe, 

N. B. The figures in the left band column refer to the numbers in the 
preceding tables, where the English names of the constellations are 
given, together with the number of stars in each, and the names of 
the principal stars : the letter N or S, immediately following the 
name of the^constellation, shows whether it be north or south of the 
zodiac; if the constellation be situated in the zodiac it has the letter 
Z annexed to it. N and S in the column marked D, point out wheth¬ 
er the middle of the constellation has north or south declination* 




K. 

D. 

19 

Andromeda. N. - . - 

14 

1 34 N. 

6 

Antinbus. N. - - - - 

292 

0 

34 

Apus, vel Avisindica. S. 

252 

75 S. 

11 

Aquarius. Z. ... - 

335 

4 S. 

6 

Aquila. N. - - - - 

295 

8 N. 

28 

Ara. S. - - - - - 

255 

ti5 S. 

1 

Aries. Z. ... - 

SO 

22 N. 

45 

Argo Navis. S. - 

115 

50 S. 

10 

Asterion et Chara. N. « - 

200 

40 N. 

S3 

A-uriga. N. . - - - 

75 

45 N. 

11 

Bootes. N. - , - - 

212 

20 N. 

12 

Brandenburgiura Sceptrura. S. - - 

67 

15 S. 

32 

Cameleopardalus. N. - 

68 

70 N. 

4 

Cancer. Z. - - - - 

128 

20 N. 

15 

Canis Major. S. ... 

105 

20 S. 

5 

Canis Minor. S. - 

120 

5 N. 

10 

Capricornus. Z. - - - 

310 

20 S. 

31 

Caput Medusse. N. ... 

44 

40 N. 

SO 

Cassiopeia. N. ... 

12 

60 N. 

20 

Centaurus. S. - - - - 

200 

50 S. 

29 

Cepheus. N. - 

338 

65 N. 

1 

Cetus. S. - 

25 

12 S. 

13 

Cerberus. N. ... 

271 

22 N. 

27 

ChamcEleon. S. - 

175 

78 S. 

23 

Circinus. S. - - - • - 

222 

64 S. 

14 

Columba Noachi. 5?. - - - 

85 

35 S. 

9 

Coma Berenices. N. ... 

185 

26 N. 

25 

Cor Caroli. N. • . - - 

191 

39 N. 

30 

Corona Australis. S. - 

278 

40 S. 

12 

Corona Borealis. N. - - - 

235 

SO N. 

19 

Corvus. S. - - . - 

185 

15 S. 

18 

Crater. S. .... 

168 

15 S. 

25 

Crux. S. .... 

183 

60 S. 

27 

Cygnus. N. - - . . 

308 

42 N, 

17 

Delphinus. N. ... 

308 

15 N. 

44 

Dorado or Xiphias. S. • - - 

75 

62 8 . 

26 

Draco. N. - - . - 

270 

66 N. 

7 

Equulus. N. .... 

316 

5 N. 

43 

Equuleus Pictorius. S. » . 

84 

55 S. 

2 . 

Eridanus. S. .... 

60 

10 S. 














DEFINITIONS, &c. 


27 




R. 

D. 

11 

Fornax Cheniica. S, - 

42 

30 S. 

3 

Gemini. Z, . - _ . 

111 

32 N. 

32 

Grus. S. - - - _ 

330 

45 S. 

13 

Hercules. N. - - - . 

255 

22 N. 

37 

Horologium. S. ... 

40 

60 S. 

6 

Hydra. S. . - - . 

139 

8 S. 

39 

Hydrus. S. - • - - 

28 

68 S. 

31 

Indus. S. , - - « 

315 

55 S. 

28 

Lacerta. N. - - * - ' 

336 

43 N. 

5 

Leo -Major. Z. - - 

150 

15 N. 

' 8 

Leo Minor. N. - . - 

150 

35 N. 

13 

Lepus. S. - . - . 

80 

18 S. 

7 

Libra. Z. - - - . 

226 

8 S, 

2 l 

Lupus. S. .... 

230 

45 S, 

34 

Lynx. N. - - ^ . 

111 

50 N, 

14 

Lyra. N* .... 

283 

38 N, 

17 

Machina Pneumatica. S. 

150 

32 S. 

8 

Microscopiuni. S. ... 

315 

35 S. 

4 

Monoceros. S. - . . 

110 

0 

1 

Mons Maenalus. N. - - . 

225 

5 N. 

41 

Mons Mens*. S. - - - 

76 

72 S. 

22 

Musca. N. » - - < - 

40 

27 N. 

26 

Musca Australis, vel Apis. S* 

185 

68 S. 

22 

Norma, vel quadra Euclidis. S. - 

242 

45 S. 

35 

Octans Hadleianus. S. - - 

310 

80 S. 

10 

Officina Sculptoria. S. - - - 

3 

38 S. 

3 

Orion. S. - - - - 

80 

0 

33 

Pavo. S. - 

302 

68 S. 

18 

Pegasus. N. - 

340 

14 N. 

31 

Perseus. N. - - - . 

46 

49 N. 

36 

Phoenix. S. - 

10 

50 S. 

1 £ 

Pisces. Z. - - - . 

5 

10 N. 

9 

Piscis notius, vel Australis. S. 

335 

30 S. 

46 

Pisces volans. S. . - - 

127 

68 S. 

42 

Praxiteles, vel cela Sculptoria, S, 

68 

40 S. 

16 

Pyxis Nautica. S, ... 

130 

30 S. 

38 

Reticuliis Rhomboidalis, S, - 

62 

62 S. 

47 

Robur Caroli. S. - - . 

159 

50 S. 

9 

Sagittarius. Z. - - - 

'285 

35 S. 

16 

.'•agitta. N, - - » - 

295 

18 N. 

7 

Sextans. S. - - - - 

5 

0 

8 

Scorpio. Z. . - - - 

244 

26 S. 

5 

Scutum Sobieski. N. - - • 

275 

10 s. 

2 

Serpens. N. . . - - 

235 

10 N. 

3 

Serpentarius. S. . - - 

260 

13 N. 

2 

Taurus. Z. . - - - 

65 

16 N. 

4 ' 

Taurus Poniatowski. N. - - 

275 

7 N. 

29 

Felescopiura. S. - 

278 

50 S. 

40 • 

Touchan. S. - 

359 

66 S. 

20 ' 

Triangulum. N. - - - 

27 

32 N. 

24 • 

Triangulum Australe. S, 

238 

65 S. 

21 

Triangulum Minus. N« • « - 

32 

28 N. 

24 

Ursa Major. N. . - - 

153 

60 N. 

23 

Ursa Minor. N. - 

235 

75 N. 

6 

Virgo. Z, - - - • 

195 

5 N. 

15 

Vulpecula et Anser. N. - 

300 

25 N. 

44 

Xiphias. 8. « - - 

75 

62 S. 



















'i8 


DEFINITIONS, &c 


Explanation of the different emblematical Figures delineated on the 
Surface of the Celestial Globe* 

I. THE CONSTELLATIONS IN THE ZODIAC. 

It is conjectured that the figures in the signs of the zodiac are de¬ 
scriptive of the seasons of the year, and that they are Chaldean or 
Egyptian hieroglyphics, intended to represent some remarkable occur¬ 
rence in each month. Thus, the spring signs were distinguished for the 
production of those animals which were held in the greatest esteem, 
viz. the sheep, the black-cattle, and the goats ; the lattei being the 
most prolific, were represented by the figure of Gemini.—When the sun 
enters Cancer, he discontinues his progress towards the north pole, and 
begins to return towards the south pole. This retrograde motion 
was represented by a Crab, which is said to go backwards. The beat 
that usually follows in the next month is represented by the Lion, an 
animal remarkable for its fierceness, and which, at this season was fre¬ 
quently impelled through thirst, to leave the sandy desert, and make 
its appearance on the banks of the Nile. The sun entered the 6th sign 
about the time of harvest, which season was therefore represented by a 
virgin or female reaper, with an ear of corn in her hand. When the 
sun enters Libra, the days and nights are equal all over the world, and 
seem to observe an equilibrium, like a balance. 

Autumn, which produces fruits in great abundance, brings with it a 
variety of diseases : this season is represented by that venomous animal 
the Scorpion, who wounds with a sting in his tail as he recedes. The 
fall of the leaf was the season for hunting, and the stars which marked 
the sun’s path at this time were represented by a huntsman, or archer, 
with his arrows and weapons of destruction. 

The Goat, which delights in climbing and ascending some mountain 
or precipice, is the emblem of the winter solstice, when the sun begins 
to ascend from the southern tropic, and gradually to increase in height 
for the ensuing half year. 

Aquarius, or the Water-bearer, is represented by the figure of a man 
pouring out water from an urn, an emblem of the dreary and uncomfort¬ 
able season of w'inter. 

The last of the zodiacal constellations was Pisces, ora couple of fish¬ 
es, tied back to back, representing the fishing season. The severity of 
the winter is over, the flocks do not afford sustenance, but the seas and 
l ivers are open, and abound with fish. 

The Chaldeans and Egyptians were the original inventors of astro¬ 
nomy ; they registered the events in their history, and the mysteries 
of their religion among the stars by emblematical figures. The Greeks 
displaced many of the Chaldean constellations, and placed such images 
as had reference to their own history in their room. The same method 
was followed by the Romans ; hence, the accounts given of the signs of 
the zodiac, and of the constellations, are contradictory and involved in 
thble. 

II. THE NORTHERN CONSTELLATIONS. 

Mows M®NAtus. The mountain Maenalus in Arcadia was sacred 
to the god Pan, and frequented by shepherds ; it received its name from 
Maanalus, a son of Lycaon, king of Arcadia. 


29 


DEFINITIONS, &c. 

Serpfns is also called Serpens Ophiuchiy being grasped by the hands 
of Ophiuchus. 

Serpentabius, Ophiuchus, or JEsculapius^ is represented with a 
large beard, and holding in his two hands a serpent. The serpent was 
the symbol of medicine, and of the gods who presided over it, as Apollo 
and jEsculapius, because the ancient physicians used serpents in their 
prescriptions. 

Taurus Poni atowski was so called in honour of Count Ponia- 
towski, a polish officer of extraordinary merit, who saved the life of 
Charles XII. of Sweden, at the battle of Pultowa, a town near the 
Dneiper, about 150 miles south-east of Kiow; and a second time at the 
island o( Rugen, near the mouth of the river Oder. 

Scutum Sobieski was so named by Hevelius, in honour of John 
Sobieski, king of Poland, Hevelius was a celebrated astronomer, born 
at Dantzick ; his catalogue of fixed stars was entitled Firmamentum 
Sobieskianum^ and dedicated to the king of Poland. 

AauiLA is supposed to have been JVlerops, a king of the island of 
Cos, one of the Cyclades; who, according to Ovid, was changed into 
an eagle, and placed among the constellations. 

Antinous was a youth of Bithynia in Asia Minor, a great favour¬ 
ite of the emperor Adrian, who erected a temple to his memory, and 
placed him among the consteliations.—Antinous is generally reckoned 
a part of the constellation Aquila. 

EauuLUs, the little horse^ or EquiSectio, the horse’s head, is supposed 
to be the brother of Pegasus. 

Leo Minor was formed out of the Stella Informes, or unformed 
stars of the ancients, and placed above Leo, the zodiacal constellation. 
Ajccording to the Greek Fables, Leo was a celebrated Nemaean lion 
which had dropped from the moon, but being slain by Hercules, was 
elevated to the heavens by Jupiter, in commemoration of the dreadful 
conflict, and in honour of that hero. But this constellation wasa- 
mongst the Ej^ptian hieroglyphics, long before the invention of the 
fables of Hercmes. See the Zodiacal constellations, page 28. Nemaea 
was a town of Argolis in Peloponnesus, and was infested by a lion which 
Hercules slew, and clothed himself in the skin : games were instituted 
to commemorate this great event. 

Coma Berenices is composed of the unformed stars, between the 
Lion’s tail and Bootes. Berenice was the wife of Evergetes, a surname 
signifying benefactor; when he went on a dangerous expedition, she 
vowed to dedicate her hair to the goddess Venus if he returned in safe¬ 
ty* Sometime after the victorious return of Evergetes, the locks which 
were in the temple of Venus disappeared; and Conon, an astronomer, 
publicly reported that Jupiter had carried them away, and made them 
a eonstellation. 

Asterionetchaba, vEL Canes Venatici, the two greyhounds, 
held in a string by Bootes ; they were formed by Hevelius out of the 
Slella Informes, of the ancient catalogues. 

Bootes is supposed to be Areas, a son of Jupiter and Calisto ; Juno, 
who was jealous of Jupiter, changed Calisto into a bear, she was near 
being killed by her son Areas in hunting. Jupiter, to prevent farther 
injury from the huntsmen, ma<]e Calisto a constellation of heaven, and 
on the death of Areas, conferred the same honour on him. Bootes is 
represented as a man in a walking pasture, grasping in his left hand a 
club, and having his right hand extended upwards, holding the cord of 
the two dogs Asterion and Chara, which seem to be barking at the 
Great Bear; hence Bootes is sometimes called the bear-driver, and the 
office assigned him is to drive the two bears round about the pole. 


:30 


DEFINITIONS, &c. 


Corona Borealis is a beautiful crown given by Bacchus, the son 
of Jupiter, to Ariadne, the daughter of Minos, second king of Crete. 
Bacchus is said to have married Ariadne after she was basely deserted 
by Theseus, king of Athens, and after her death the crown which 
Bacchus had given her was made a constellation. 

Hercules is represented on the Celestial globe holding a club in 
his right hand, the three-headed dog, Cerberus, in his left, and the skin of 
the Nemaean Lion thrown over his shoulders. Hercules was the son of 
Jupiter and Alcmena, and reckoned the most famous hero in antiquity. 

Cerberus was a dog belonging to Pluto, the god of the infernal 
regions; this dog had fifty heads, according to Hesiod, and three ac¬ 
cording to other raythologists: he was stationed at the entrance of the 
infernal regions, as a watchful keeper, to prevent the living from enter¬ 
ing, and the dead from escaping from their confinement. The last and 
most dangerous exploit of Hercules was to drag Cerberus from the in¬ 
fernal regions, and bring him before Eurysiheus, king of Argos. 

Lyra, the lyre or harp, is included in Vultur Cadens. This constel¬ 
lation was at first a tortoise, afterwards a lyre, because the strings of 
the lyre were originally fixed to the shell of the tortoise : it is asserted 
that this is the lyre which Apollo or Mercury gave to Orpheus, and 
with which he descended the infernal regions, in search of bis wife Eu- 
rydice. Orpheus, after death, received divine honours ; the Muse# 
gave an honourable burial to his remains, and his lyre became one of 
the constellations. 

Vulpecula et Anser, the Fox and the Goose, was made by He- 
velius out of the unformed stars of the ancients. 

Sagitta, the Arrow. The Greeks say that this constellation owes 
its origin to one of the arrows of Hercules, with which he killed the ea¬ 
gle or vulture that perpetually gnawed the liver of Prometheus, who 
was tied to a rock on Mount Caucasus, by order of Jupiter. 

Delphi vus, the dolphin, was placed among the constellations by 
Neptune, because, by means of a dolphin, Amphitrite be|^me the wife of 
Neptune, though she had made a vow of perpetual celibacy. 

Pegasus, the winged horse, according to the Greeks, sprung from 
the blood of the Gorgon Medusa, after Perseus, a son of Jupiter, had 
cut off her head. Pegasus fixed his residence on Mount Helicon in 
Boeotia, where, by striking the earth with his foot, he produced a foun¬ 
tain called Hippocrene. He became the favourite of the Muses, and 
being afterwards tamed by Neptune, or Minerva, he was given to Bel- 
lerophon to conquer the Chimaera, a hideous monster that continually 
vomited flames : the foreparts of its body were those of a lion, the mid¬ 
dle was that of a goat, and the hinderparts were those of a dragon ; it 
had three heads, viz, that of a lion, a goat, and a dragon. After the de¬ 
struction of this monster, Bellerophon attempted to fly to heaven upon 
Pegasus, but Jupiter sent an insect which stung the horse, so that he 
threw down the rider. Bellerophon fell to the earth, and Pegasus con¬ 
tinued his flight up to heaven, and was placed by Jupiter among the 
constellations. 

Andromeda is represented on the celestial globe by the figure of 
a woman almost naked, having her arms extended, and chained by the 
wrist of her right arm to a rock. She ws’ the daughter of Cepheus, king 
of ^Ethiopia, who, in order to presence his kingdom, was obliged to tie 
her naked to a rock near Joppa, now Jaffa, in Syria, to be devoured by 
a sea-monster; but she was rescued by Perseus, in his return from the 
conquest of the Gorgons, who turned the monster into a rock by show¬ 
ing it the bead of Medusa. Andromeda was made a constellation after 
her death, by Minerva. 


DEFINITIONS, &c. 


31 


TBiANGtJLUM. A triangle is a well known figure in geometry; it 
was planed in the heavens in honour of the most fertile part of Egypt, 
being called the delta of the Nile, from its resemblance to the Greek let¬ 
ter of that name The invention of Geometry is usually ascribed to 
the Egyptians, and it is asserted that the annual inundations of the Nile, 
which swept away the bounds and land-marks of estates, gave occasion 
to it, by obliging the Egyptians to consider the figure and quantity be¬ 
longing to the several proprietors. 

Ursa Major, is said to be Calisto, an attendant of Diana, the god¬ 
dess of hunting. Calisto was changed into a bear by Juno.— Seethe. 
Constellation Bootes. —It is farther stated that the ancients represented 
Ursa Major and Ursa Minor, each under the form of a wagon, drawn, 
by a team of horses. Ursa Major is well known to the country people 
at this day by the title of Charlesh Wain or wagon ; in some places it 
is called the Plough. There are two remarkable stars in Ursa Major, 
considered as the hindmost in the square of the wain, called the point¬ 
ers. because an imaginary linedrawm through these stars and extended 
upwards will pass near the pole star in the tail of the Little Bear. 

Cob CAKOLi,’or Charles’s heart, in the neck of Chara, the southern¬ 
most of the two dogs held in a string by Bootes, was so denominated 
by Sir Charles Scarborough, physician to king Charles 11. in honour of 
king Charles 1 . 

Draco. The Greeks give various accounts of this constellation ; by 
some it is represented as the watchful dragon which guarded the golden 
apples in the garden of the Hesperides, near Mount Atlas in Vfrica; 
and was slain by Hercules : Juno, who presented these apples to Jupiter 
on the day of their nuptials, took Draco up to heaven, and made a con- 
stellation.of it as a reward for its faithful services; others maintain, 
that in a war with the giants, this dragon was brought into combatj, 
and opposed to Minerva, who seized it in her handstand threw it, twist¬ 
ed as it was, into the heavens round the axis of the earth, before it had 
time to unwind its contortions. 

CvGNirs is fabled by the Greeks to be the swan under the form of 
which Jupiter deceived Leda, or Nemesis, the wife of Tyndarus, king 
of Laconia. Leda wms the mother of Pollux and Helena, the most 
beautiful woman of the age ; and also of Castor and Clytemnestra. 
The two former were deemed the offspring of Jupiter, and the others 
claimed Tyndarus as their father. 

Lacebta, the lizard, was added by Hevelius to the old constella¬ 
tions. 

Cassiopeia was the wife of Cepheus, and mother of Andromeda. 
See these constellations., as also Cetus. 

Cepheus was a king of .Ethiopia, and the father of Andromeda by 
Cassiopeia ; Cepheus was one of the Argonauts who went with Jason 
to Colchis to fetch the golden fleece. 

Perseus is represented on the globe with a sword in his right hand, 
the head of Medusa in his left, and wings at his ancles. Perseus was 
the son of Jupiter and Danae. Pluto, the god of the infernal regions, 
lent him his helmet, which had the power of rendering its bearer invisi¬ 
ble ; Minerva, the goddess of wisdom, furnished him with her buckler, 
which was resplendent as glass ; and he received from Mercury wings 
and a dagger or sword ; thus equipped, be cut off the head of Medusa, 
and from the blood which dropped from it in his passage through the 
air, sprang an innumerable quantity of serpents which ever after infest¬ 
ed the sandy deserts of Lybia. Medusa was one of the three Gorgons 
who had the power to turn into stones all those on whom they fixed 
their eyes; Medusa was the only one subject to mortality ; she was 


32 


DEFINITIONS, kc, 


celebrated for the beauty of her locks, but having violated the sanctity 
of the temple of Minerva, that goddess changed her locks into serpents. 
Ste the constellalion Andromeda. 

Cameleopardalus was fornted by Hevelius. The Cameleopard is 
remarkably tame and tractable; its natural properties resemble those 
of the camel, and its body is variegated with spots like the leopard. 
This animal is to be found in Ethiopia and other parts of Africa; its 
neck is about seven feet long, its fore and hind legs from the hoof to the 
second joint are nearly of the same length; but from the second joint 
of the legs to the body, the forelegs are so long in comparison w'ith the 
hind ones, that the body seems to slope like the roof of a house. 

Auriga is represented on the celestial globe, by the figure of a 
man in a kneeling or sitting posture, with a goat and her kids in his 
left hand, and a bridle in his right. The Greeks give various accounts 
of this constellation ; some suppose it to be Erichthonius, the fourth 
king of Athens, and son of Vulcan and Minerva ; he was very deform¬ 
ed, and his legs resembled the tails of serpents; he is said to have in¬ 
vented chariots, and the manner of harnessing horses to draw them. 
Others say that Auriga is Mirtilus, a son of Mercury and Phaetusa; 
he was charioteer to (Enomaus, king of Pisa, in Elis, and so experienced 
in riding and the management of horses, that he rendered those of 
CEnomaus the swiftest in all Greece: his infidelity to his master pro¬ 
ved at last fatal to him, but being a son of Mercury, he was made a con¬ 
stellation after his death. But as neitherof these fables seem to account 
for the goat and her kids, it has been supposed that they refer to A- 
malthxa, daughter of Melissus, king of Crete, who, in conjunction with 
her sister Melissa, fed Jupiter with goat’s milk ; it is moreover said, 
that Amalthsea was a goat called Olenia, from its residence at Olenus, 
a town of Peloponnesus. 

The Lynx was composed by Hevelius out of the unformed stars of 
the ancients, between Auriga and Ursa Major. 


III. THE SOUTHERN CONSTELLATIONS. 

Cetus, the whale, is pretended by the Greeks to be the sea-monste/ 
which Neptune, brother to Juno, sent to devour Andromeda; because 
her mother, Cassiopeia, had boasted herself to be fairer than Juno and 
the Nereides. 

Eridanits, the river Po, called by Virgil the king of rivers, was 
placed in the heavens for receiving Phaeton, whom Jupiter struck 
with thunder-bolts when the earth was threatened with a general con¬ 
flagration, through the ignorance of Phaeton, who had presumed to be 
able to guide the chariot of the sun. The Po is sometimes called Orion’s 
river. 

Orion is represented on the globe by the figure of a man with a 
sword in his belt, a club in his right hand, and a skin of a lion in his 
left hand; he is said by some authors to be the son of Neptune and 
Euryale, a famous huntress ; he possessed the dispusitiou of his moth¬ 
er, became the greatest hunter in the world, and boasted that there 
was not any animal on the earth which he could not conquer. Others 
say, that Jupiter, Neptune, and Mercury, as they travelled over Bceo- 
tia, met with great hospitality from Hyrieus. a peasant of the country^ 
who was ignorant of their dignity and character. When Hyrieus had 
discovered that they were gods, he welcomed them by the vohin- 
tary sacrifice of an ox. Pleased with his piety, the gods promised - to 
grant him whatever he required, and the Oldman who bad lately lost 


DEFINITIONS, &c. 


33 


his wife, and to whom he made a promise never to marry again, desired 
them that, as he was childless, they would give haii a son without o- 
bliging him to break his promise. The gods consented, and Orion was 
produced from the hide of an ox. 

Monoceros, the Unicorn, was added by Hevelius, and composed of 
stars which the ancients had not comprised within the outlines of the 
other constellations. 

CA.NIS Minor, the Little Dog, according to the Greek fables, is 
one of Orion’s hounds; but the Egyptians were most prebably ihe in¬ 
ventors of this constellation, and as it rises before the dog star, which, 
at a particular season was so much dreaded; it is properly represented 
as a little watchful creature, giving notice of the other’s approach; 
hence, the Latins have called it Antecanis, the star before the dog. 

Hydra is the water serpent, which, according to poetic fable, infested 
the lake Lerna in Peloponnesus: this monster had a great number of 
heads, and as soon as one w as cut off another grew in its stead ; it w as 
killed by Hercules. The general opinion is, that this Hydra was only 
a multitude of serpents which infested the marshes of Lerna. 

Sextans, the .'•extant, a mathematical instrument well known to 
mariners, was formed by Hevelius from the Stellce Infonnes of the an¬ 
cients. 

Microscopittm, the Microscope, is an optical instrument composed 
of lenses or mirrors, so arranged, that by means of which very minute 
objects may be clearly and distinctly viewed. 

Piscis AUSTRALIS, the southern fish, is supposed by the Greeks to 
be Venus, who transformed herself into a fish, to escape from the ter¬ 
rible giant Typhon. 

Lepus, the hare, according to the Greek fables was placed near Ori¬ 
on, as being one of the animals which he hunted. 

Cams Major, the Great Dog, according to the Greek fables is one 
of Orion’s hounds; (See Canis Minor) but the Egyptians, who careful¬ 
ly watched the rising of this constellation, and by it judged of the swel¬ 
ling of the Nile, called the bright star Sirius, the centinel and watch of 
the year: and, according to their hieroglyphical manner of writing, rep¬ 
resented it under the figure of a dog. The Egyptians called the Nile 
Siris^ and hence is derived the name of their deity Osiris. 

CoRVUs, the Crow, was. according to the Greek fables, made « con¬ 
stellation by Apollo; this god being jealous of Coronis(the daughter of 
Phlegyas and mother of .^Esculapius) sent a crow to watch her beha¬ 
viour : the bird, perched on a tree, perceived her criminal partiality to 
Ischys. the Thessalian, and acquainted Apollo with her conduct. 

Centaurus. The Centauri were a people of Thessaly, half men and 
half horses. The Thessalians were celebrated for their skill in taming 
horses, and their appearance on horseback was so uncommon a sight 
to the neighbouring states, that at a distance they imagined the man 
and horse to be one animal: when the Spaniards landed in America 
and appeared on horseback, the Mexicans had the same ideas This 
constellation is by some supposed to represent Chiron the Centaur, tu¬ 
tor of Achilles, -tEsculapius, Hercules, &c.; but as Sagittarius is like¬ 
wise a Centaur, others have contended that Chiron is represented by 
Sagittarius. 

Crux, Crusero or Crosier. There are four stars in this constel¬ 
lation forming a cross, by which mariners, sailing in the southern hem¬ 
isphere, readily find the situation of the Antarctic pole. 

Ara is supposed to be the altar on which the gods swore before their 
combat with the giants. 


7 


34 


DEFINITIONS, &c. 


Argo N avis is said to be the ship Argo, which carried Jason and 
the Argonauts to Colchis to fetch tiie golden fleece. 

Robur Caboli, or Charles’s Oak, was so called by Dr. Halley, in 
memory of the tree in which Charles II. saved himself from his pursuers, 
after the battle of Worcester. Dr Halley went to Si. Helena, in the 
year 1676, to take a catalogue of such stars as do not rise above the 
horizon of London. 

91. Galaxy, via lactea, or Milky‘Way, is a 
whiiiish, luminous trac , which seems lo encompass the 
hea vens like a girdle, oi a C'^nsiderabie, though une¬ 
qual breadth, varying from about 4 to 20 degrees, li is 
composed of an infinite number of small stars, which by 
their joint liglit, occasion that confused whiteness which 
we perceive in a clear night, when the moon does not 
shine very bright. The Milky-way may be traced on 
the celestial globe, beginning at Cygnus, through Ce- 
pheus, Cassiopeia, Perseus, Auriga, Orion’s club, the 
feel of Gemini, part of Monoceros, Argo Navis, Robur 
Caroli, Crux, the feet of the Centaur, Circinus, Quadra 
Euclidis, and Ara ; here it is divided into two parts ; 
the eastern branch passes through the tail of Scorpio, 
the bow of Sagittarius, Scutum Sobieski, the feet of An- 
tinous, Aquila, Sagitta, and Vulpecula ; the western 
branch passes through the upper part of the tail of 
Scorpio, the right side of Serpentarius, Taurus Ponia- 
towski, the Goose, and the neck of Cygnus, and meet^ 
the aforesaid branch in the body of Cygnus. 

92. Nebulous, or cZoiid?/, is a term applied to cer¬ 
tain fixed stars, smaller than those of the 6th magnitude, 
which only show a dim hazy light like little specks or 
clouds. In Prajsepe, in the breast of Cancer, are reckon¬ 
ed 36 little ^ta^s ; F. le Compte adds, that there are 40 
such stars in the Pleiades, and 2500 in the whole constel¬ 
lation of Orion. It may be further remarked, that the 
Milky-way is a continued assemblage of Nebulae. 

93. Bayer’s characters. John Bayer, of Augs¬ 
burg in Swabia, published in 1603 an excellent work, 
entitled Uranometria^ being a complete celestial atlas of 
all the constellations, with the useful invention of de¬ 
noting the stars in every constellation by the letters of 
the Greek and Roman Alphabets ; setting the first 
Greek letter « to the principal star in each constellation, 
^ to the second in magnitude, y to the third, and so on, 
and when the Greek alphabet was finished, he began 
with a, b, c, &c. of the Roman. This useful method 


DEFINITIONS, &c. 


35 


of describing the stars has been adopted by all succeed¬ 
ing aslronoiners, who have farther enlarged it by adding 
the numbers, 1, 2,3, &c. in the same regular succession, 
when any constellation contains more stars than can be 
marked by the two alphabets. The figures are, how¬ 
ever, sometimes placed above the Greek letter, espe¬ 
cially where double stars occur, for though many sfars 
may appear single to the naked eye, yet, when viewed 
through a telescope of considerable magnifying power, 
they appear double, triple, &c. Fluis in Dr Zach’sTa- 
bulee Mofuum, Solis, we meet with f Tauri, /3 Tauri, 
Tauri, Tauri, &c. 

As the Greek letters so frequently occur in catalogue^ of the stars and 
on the celestial globes, the Greek alphabet is here introduceil for the 
use of those who are unacquainted with the letters. The capitals are 
seldom used in the catalogue of stars, but are here given for the sake of 
regularity. 

THE GREEK ALPH ABET, 


A 

Ci 

Alpha 

a 

B 


Beta 

b 

r 

yf 

Gamma 

g 

A 


Delta 

d 

E 

e 

Epsilon 

e short 

Z 

s'? 

Zeta 

z 

H 


Eta 

e long 

© 


Theta 

th 

I 

t 

Iota 

i 

K 

K 

Kappa 

k 

A 

A 

Lambda 

1 

M 

A* 

Mu 

m 

N 

y 

Nu 

n 

A 

1 

X 

X 

o 

0 

Omicron 

0 short 

n 


Pi 

P 

p 

ep 

Rho 

r 

s 


Sigma 

s 

T 

f? 

Tau 

t 

T 

if 

TJpsilon 

u 

O 


Phi 

ph 

X 

X, 

Chi 

ch 



Psi 

ps 

12 

a 

Omega 

o long 


94. Planets are opaque bodies, similar to our earth, 
which move round the sun in certain periods of time* 


36 


DEFINITIONS, kc. 


They shine not by their own light, but by the reflection 
of the light which they receive from the sun. The 
planets are distinguished into primary and secondary. 

95. The Primary planets regard the sun as their 
centre of motion. There are 7* Primary planets, dis¬ 
tinguished by the following characters and names, viz. 
5 Mercury, $ Venus, 0 the earth, S Mars, “U Jupi¬ 
ter, ]2 Saturn, and ^ the Georgium Sidus. 

96 The Secondary planets, satellites or moons, 
regard the primary planets as their centres of motion : 
thus the moon revolves round the Earth, the satellites of 
Jupiter move round Jupiter, &c. There are 18 secon¬ 
dary planets. The earth has one satellite, Jupiter/our, 
Saturn seven, and the Georgium Sidus six» 

97. The Orbit of a planet is the imaginary path it 
describes round the sun. The earth’s orbit is the 
ecliptic. 

98. Nodes are the two opposite points where the 
orbit of a planet seems to intersect the ecliptic. That 
where the planet appears to ascend from the south to 
the north side of the ecliptic, is called the ascending or 
north node, and is marked thus ^ ; and the opposite 
point where the planet appears to decend from the north 
to the south, is called the decending or south node, and 
is marked 

99. Aspect of the stars or planets, is their situation 
with respect to each other. There are five aspects, 
viz. 6 Conjunction, when they are in the same sign 
and degree ; ^ Sextile, when they are two signs, or a 
sixth part of a circle, distant; □ Quartile, when they 
are three signs, or a fourth part of a circle, from each 
other; ^ Trine, when they are four signs, or a third 
part of a circle, from each other ; § Opposition, when 
they are six signs, or half a circle, from each other. 

The conjunction and opposition (particularly of the 
moon) are called the Syzygies ; and the quartile aspect, 
the Quadratures, 


* An eighth primary planet called Ceres, was discovered by M. Piaz- 
zi of Palermo, in Sicily, on the first of January 1801 ; a ninth called 
Pallas, was discovered by Dr. Olbei s, of Bremen, on the 28th of March, 
1802; and others have since been discovered. See Part II. Chap. 1. 



DEFINITIONS, &c. 


37 


100. Direct. A planet’s motion is said to be di¬ 
rect when it appears (to a spectator on the earth) to go 
forward in the zodiac accord ng to the order of the signs. 

101. Stationary. A planet is said to be station¬ 
ary, when (to an observer on the earth) it appears for 
some time in the same point of the heavens. 

102. Retrograde. A planet is said to be retrograde, 
when it apparently goes backward, or contrary to the 
order of the signs. 

103. Digit, the twelfth part of the sun or moon’s 
apparent diameter. 

104. Disc, the face of the sun or moon, such as they 
appear to a spectator on the earth ; for though the sun 
and moon be really spherical bodies, they appear to be 
circular plains. 

105. Geocentric latitudes and longitudes of the 
planets, are their latitudes and longitudes as seen from 
the earth. 

106. Heliocentric latitudes and longitudes of the 
planets, are their latitudes and longitudes, as they would 
appear to a spectator situated in the sun. 

lor. Apogee or Apogseum is that point in the orbit 
of a planet, the moon, &c. which is farthest from the 
earth. 

108. Perigee or Perigaeum is that point in the orbit 
of a planet, the moon, &c. which is nearest to the earth. 

109. Aphelion or Aphelium is that point in the 
orbit of the earth, or of any other planet, which is far¬ 
thest from the sun. This point is called the higher 
Apsis. 

110. Perihelion or Perihelium is that point in the 
orbit of the earth, or of any other planet, which is near¬ 
est to the sun. This point is called the lower Apsis. 

111. Line of the apsidesIs a straight line joining 
the higher and lower Apsis of a planet; viz. a line join¬ 
ing the Aphelium and Perihelium. 

112. Eccentricity of the orbit of any planet is the 
distance between the sun and the centre of the planet’s 
orbit. 

113. Occultation is the obscuration or hiding from 
our sight any star or planet, by the interposition of the 
body of the moon, or of some other planet. 

114. Transit is the apparent passage of any planet 


38 


DEFINITIONS, &ci 


over the face of the sun, or over the face of another 
planet. Mercury and Venus, in iheir transits over the 
sun’s disc, appear like dark specks. 

115. Eclipse of the sun is an occultation of part 
of the face of the sun, occasioned by an interposition of 
the moon between the earth and the sun ; consequent¬ 
ly all eclipses of the sun happen at the time of new moon. 

116. Eclipse of the moon is a privation of the 
light of the moon, occasioned by an interposition of the 
earth between the sun and the moon; consequently all 
eclipses of the moon happen at full moon. 

Ilf. Elongation of a planet is the angle formed 
by two lines drawn from the earth, the one to the suit 
and the other to the planet*. 

118. Diurnal arch is the arch described by the 
sun, moon, or stars, from their rising to their setting.— 
The sun’s semi-diurnal arch is the arch described in 
half the length of the day. 

119. Nocturnal arch is the arch described by the 
sun, moon, or stars, from their setting to their rising. 

120. Aberration is an apparent motion of (he celes¬ 
tial bodies, occasioned by the earth’s annual motion in 
its orbit, combined with the progressive motion of light. 

121. Centripetal force is that force with which 
a moving body is perpetually urged towards a centre, 
and made to revolve in a curve instead of proceeding in 
a straight line, for all motion is naturally rectilinear.— 
Centripetal force, attraction, and gravitation, are terms of 
the same import. 

122 Centrifugal force is that force with which a 
body revolving about a centre, or about anofier body, 
endeavours to recede from that centre, or body.—There 
are two kinds of centrifugal force, viz. that which is given 
to bodies moving round another body as a centre, usual¬ 
ly called the Projectile Forces and that which bodies 
acquire by revolving upon their own axis. Thus for 
example, the annual orbit of the earth round the sun is 


* This and some of the preceding definitions are given to illustrate 
the S8th and S9th pages of Whitens Epheraeris, called Speculum Fhce- 
nomenorum. The words ctong, max. signify the greatest elongation of 
a planet. In plate II Fig. 2. E represents the earth, V Venus, and S 
the Sun. The elongation is the angle VES, measured by the arch VS, 



GEOGRAPHICAL THEOREMS. 


39 


described by the action of the centripetal and projec¬ 
tile lorces :—And, the diurnal rotation of the earth 
on its axis skives to all its parts a centrifugal force pro¬ 
portional to its velocity. Sir Isaac Newton has de* 
nionstrated, that the “ centrifugal force of bodies at 
the equator, is to the centrifugal force with which the 
bodies recede from the earth, in the latitude of Paris, in 
the duplicate ratio of the radius to the co-sine of the 
latitude. And, that the centripetal power in the lati¬ 
tude of Paris, is to the centrifugal lorceat the equator, 
as 289* is to 1.’’ 

GEOGRAPHICAL THEOREMS. 

1. THE latitude of any place is equal to the eleva¬ 
tion of the polar star (nearly) above the horizon; and 
the elevation of the equator above the horizon, is equal 
to the complement of the latitude, or what the latitude 
wants of 90 degrees. 

2. All places lying under the equinoctial, or on the 
equator have no latitude, and all places situated on the 
first meridian have no longitude; consequently, that par¬ 
ticular point on the globe where the first meridian inter¬ 
sects the eqqator, has neither latitude nor longitude. 

3. The latitudes of places increase as their distances 
from the equator increase. The greatest latitude a 
place can have is 90 degrees. 

4 The longitudes of places increase as their distan¬ 
ces from the first meridian increase, reckoned on the 
equator. The greatest longitude a place can have is 
180 degrees, being half the circumference of the globe 
at that place; hence, no two places can be at a greater 
distance from each other than 180 degrees. 

5. The sensible horizon of any place changes as often 
as we change the place itself. 

6. All countries upon the face of the earth, in respect 
to time, equally enjoy the light of the sun, and are equal¬ 
ly deprived of the benefit of it ;that is, every inhabitant 


*Princip. Prop. XIX, Book III. 



10 


GEOGRAPHICAL THEOREMS. 


of the earth has the sun aboTe his horizon for six months^ 
and below the horizon for the same length of time.* 

7. In all places of the earth, except exactly under 
the poles, the days and nights are of an equal length 
(viz. 12 hours each) when the sun has no declination, 
that is, on the 21st of March, and on the 23d of Sep¬ 
tember. 

8. In all places situated on the equator, the days and 
nights are always equal, notwithstanding the alteration 
of the sun’s declination from north to south, or from 
south to north. 

9. In all places except those on the equator, or at the 
two poles, the days and nights are never equal, but 
when the sun enters the signs of Aries and Libra, viz. 
on the 21st of March, and on the 23d of September. 

10. In all places lying under the same parallel of lati¬ 
tude, the days and nights, at any particular time, are 
always equal to each other. 

11. The increase of the longest days from the equa¬ 
tor northward or southward, does not bear any certain 
ratio to the increase of latitude ; if the longest days in¬ 
crease equally, the latitudes increase unequally. This 
is evident from the table of climates. 

12. To all places in the torrid zone, the morning and 
evening twilight are the shortest ; to all places in the 
frigid zones the longest; and to all places in the temp¬ 
erate zones, a medium between the two. 


^ This, though nearly true, is not accurately so. The refraction in 
high latitudes is very considerable (see definition 85th) and near the 
poles the sun will be seen for several days before he comes above the 
horizon; and he will, for the same reason, be seen for several days 
after he has descended below the horizon.—The inhabitants of the 
poles (if any) enjoy a very large degree of twilight, the sun being near¬ 
ly two months before he retreats 18 degrees below the horizon, or to 
the point where his rays are first admitted into the atmosphere, and he 
is only two months more before he arrives at the same parallel of lati¬ 
tude : and particularly near the north-pole, the light of the moon is 
greatly increased by the reflection of the snow, and the brightness of 
the Aurora Borealis: the sun is likewise about seven days longer in 
passing through the northern, than through the southern signs; that is, 
from the vernal equinox, which happens on the ‘^Ist of March, to the 
autumnal equinox, which falls on the 2Sd of September, being the sum¬ 
mer half-year to the inhabitants of north latitude, is 186 days; the win¬ 
ter half-year is therefore only 1T9 days. The inhabitants near the 
north-pole have consequently more light in the course of a year than 
any other inhabitants on the surface of the globe. 



GEOGRAPHICAL THEOREMS. 


4i 


13. To all places lying within the torrid zone, the sun 
is vertical twice a year ; to those under each tropic once, 
but to those in the temperate and frigid zones, it is nev¬ 
er vertical. 

14. At all places in the frigid zones, the sun appears 
every year wilhoul setting for a certain number ot days, 
and disappears for nearly the same space of time ; and 
the nearer the place is to the pole the longer the sun 
continues without setting ; viz. the length of the longest 
days and nights increases, the nearer the place is to the 
pole. 

15. Between the end of the longest day, and the be¬ 
ginning of the longest night, in the frigid zone, and be¬ 
tween the end of the longest night, and the beginning of 
the longest day, the sun rises and sets as at other places 
on the earth. 

16. At all places situated under the arctic or antarc¬ 
tic circles, the sun, when he has 23“ 28' declination, 
appears for 24 hours without setting ; but rises and sets 
at all other times of the year. 

17. At all places between the equator and the north- 
pole, the longest day and the shortest night are when the 
sun has (23“ 28') the greatest north declination, and the 
shortest day and longest night are when the sun has 
the greatest south declination. 

18. At all places between the equator and the south- 
pole, the longest day and the shortest night are when the 
sun has (23° 28') the greatest south declination ; and 
the shortest day and longest night are when the sun has 
the greatest north declination. 

19. At all places situated on the equator, the shadow 
at noon of an object, placed perpendicular to the hori¬ 
zon, falls towards the north for one half of the year, and 
towards the south the other half. 

20. The nearer any place is to the torrid zone, the 
shorter the meridian shadow of objects will be. When 
the sun’s altitude is 45 degrees, the shadow of any par¬ 
ticular object is equal to its height. 

21. The farther any place (situated in the temperate 
or torrid zones) is from the equator, the greater the ris¬ 
ing and setting amplitude of the sun will be. 

22. All places situated under the same meridian,so far 
as the globe is enlightened, have noon at the same time, 

8 


42 dENER \L PROPERTIES OF MATTER. 


23. If a ship set out from any port, and sail round the 
earth eastward to the same port again, the people in ihat 
ship in reckoning their time, will gain one complete day 
at their return, or count one day more than those who 
reside at the same port. If they sail westward they will 
lose one day, or reckon one day less. To illustrate this, 
suppose the person who travels westward should keep 
pace with the sun, it is evident he would have continual 
day, or it would be the same day to him durmg his lour 
round the earth.; but the people who remained at the 
place he departed from, have had night in the same 
time, consequently they reckon a day more than he does. 

24. Hence, if two sh^ps should set out at the same 
lime, from any port, and sail round the globe, the one 
eastward and the other westward, so as to meet at the 
same port on any day whatever, they will differ two 
days in reckoning their time at their return. If they 
sail twice round the earth they will differ four days ; if 
thrice, six, &c. 

25. But, if two ships should set out at the same time 
from any port and sail round the globe, northward, or 
southward, so as to meet at the same port on any day 
whatever, they will not differ a minute in reckoning 
their time, nor from those who reside at the port. 

CHAPTER II. 

Of the General Properties of Matter and the Laws of 
Motion. 

1. M ATTER is a substance which, by its different 
modifications, becomes the object of our five senses ; 
viz. whatever we can see, hear, feel, taste, or smell, 
must be considered as matter, being the constituent 
parts of the universe. 

2. The PROPERTIES OF M4TTER are extension, fig¬ 
ure, solidity, motion, divisibility, gravity, and vis iner¬ 
tia. These properties, which Sir Isaac Newton ob- 
serves=^ are the foundation of all philosophy, extend 
to the minutest particles of matter. 


* Newton’s Princip. Bqok IIL—The third rule of reasoning in phi¬ 
losophy. 



general properties of matter. 43 


3. Extension, when considered as a property of 
matter, has lengtli, breadth, and thickness. 

4. Figure is the boundary of extension ; for every 
finite extension is terminated by, or comprehended un¬ 
der, some figure. 

5. Solidity is that property of matter by which it 
fills space ; or, by which any portion of matter excludes 
every other portion from that space which it occupies. 
This is sometimes defined the impenetrability of matter. 

6. Motion Though matter of itself has no ability to 
move ; yet as all bodies, upon which we can make suit¬ 
able experiments, have a capacity of being transferred 
from one place to another, we infer that motion is a qua¬ 
lify belonging to all matter. 

r. Divisibilui’y of matter signifies a capacity of be¬ 
ing separated into parts, either actually or mentally. 
That matter is thus divisible, we are convinced by daily 
experience, but bow far the division can be actually 
carried on is not easily seen. The parts of a body may 
be so far divided as not to be sensible to the sight; and 
by the help of microscopes we discover myriads of or¬ 
ganized bodies totally unknown before such instruments 
were invented. A grain of leaf gold will cover fifty 
square inches of surface,* and contains two millions of 
visible parts : but the gold which covers the silver 
wire, used in making gold lace, is spread over a surface 
twelve times as great. From such considerations as 
these, we are led to conclude, that the division of mat¬ 
ter is carried on to a degree of minuteness far exceed¬ 
ing the bounds of our faculties. 

Mathematicians have shown that a line may be inde¬ 
finitely divided, as follows : 

Draw any line AC, and another BMA 
perpendicular to it, of an unlimited^ 
length towards Q,; and from any point/ 

D, in AC, draw DE parallel to BM. 

Take any number of points, P, O, N, 

M, in BQ,; then from P as a centre, 
andthe distance PB, describe the arch 
Bp, and in the same manner with O, 

N, M, as centres, and distances OB, 



AUamB’ Natural and Experimeatai PkUospphy. Lect. XXIV, 






44 


GENERAL PROPERTIES OF MATTER. 


NB, and IMB, describe ihe arches Bo, B?i, Bm. Now 
il is evident the farther the centre is taken from B, the 
nearer the arches will approach to D, and the line ED 
will be divided into parts, each smaller than the preced¬ 
ing one ; and since the line BM may be extended to an 
indefinite distance beyond Q,, the line ED may be indefi¬ 
nitely diminished, yet it can never be reduced to 
nothing, because an arch of a circle can never coincide 
with the straight line BC, hence it follows that ED may 
be diminished ad infinitum, 

8. Gravity is that force by which a body endeavours 
to descend towards the centre of the earth. By this 
power of attraction in the earth, all bodies on every part 
of its surface are prevented from leaving it altogether, 
and people move round it in all directions, without any 
danger of falling from it.—By the influence of attraction, 
bodies, or the constituent parts of bodies accede, or 
have a tendency to accede to each other, without any 
sensible material impulse, and this principal is univer¬ 
sally disseminated through the universe, extending to 
every particle of matter. 

9. Vis iNERTiiE is that innate force of matter by which 
it resists any change. VVe cannot move the least par¬ 
ticle of matter without some exertion, and if one portion 
of matter be added to another, the inertia of the whole is 
increased ; also, if any part be removed, the inertiais di¬ 
minished. Hence, the vis inertia of any body is propor¬ 
tional to its weight. 

10. Absolute and relative motion. A body is 
said to be in absolute motion, when its situation is chan¬ 
ged with respect to some other body, or bodies at rest ; 
and to be relatively in motion, when compared with 
other bodies which are likewise in motion. 

When a body always passes over equal parts of space 
in equal successive portions of time, its motion is said 
to be uniform. 

When the successive portions of space, described in 
equal times, continuallv increase, the motion is said to 
be accelerated ; and if the successive portions of space 
coiitimially decrease, the motion is said to be retarded. 
Also, the motion is said to be uniformly accelerated 
or retarded, when the increments or decrements of the 
spaces, described in equal successive portions of time, 
are always equal. 


LAWS OF MOTION. 


45 


11. The Velocity of a bodj, or the rate of its mo¬ 
tion, is measured by the space uniformly described in a 
given time. 

12. Force. Whatever changes, or tends to change, 
the state of rest, or motion of a body, is caljed /orce. If 
a force act but for a moment, it is called the force of 
percussion or impulse ; if it act constantly, it is called 
an accelerative force ; if constantly and equally, it is 
called an uniform accelerative force. 


GENERAL LAWS OF MOTION. 


Law I.—“ Every body perseveres in its state of rest, 
“ or uniform motion in a right line, unless it is 
compelled to change that state by forces impressed 
“ thereon,^'* —iScwton’s Princip. Book 1. 


Thus, when a body A is positively a 
at rest, if no external force put it in^'^ 


put it in ^ 3 

motion, it will always continue at rest. 

But if any impulse be given to it in the direction AB, 
unless some obstacle, or new force, stop or retard its 
motion, it will continue to move on uniformly, for ever 
in the same direction AB.—Hence any projectile, as a 
ball shot from a cannon, an arrow from a bow, a stone 
cast from a sling, &c. would not deviate from its first 
direction, or tend to the earth, but would go off from it 
in a straight line with an uniform motion, if the action of 
gravity and the resistance of the air did not alter and 
retard its motion. 


Law II. “ The alteration of motion, or the motioA 
“ generated or destroyed^ in any body, is propor- 
“ tional to the force applied ; and is made in the di- 
“ rection of that,straight line in which the force acts*” 
Newton’s princip. Book I. 


Thus, if any motion be generated by a given force, a 
double motion will be produced by a double force, a triple 
motion by a triple force, &c.—and considering motion 
as an effect, it will always be found that a body receives 
its motion in the same direction with the cause that acts 



40 


LAWS OF MOTION. 


upon it.—If the causes of motion be various, and in dif¬ 
ferent directions, the body acted upon must take an 
oblique or compound direction. Hence, a curvilinear 
motion cannot be produced by a simple cause, but must 
arise from the joint eftect of ditferent causes, acting at 
the same instant upon the body. 

Law III. “ To every action there is always opposed 
“ an equal re-action ; or the mutual actions of two 
“ bodies upon each other are always equal, and di- 
reeled to contrary points^ INewton’s Princip. 

Book 1. 

If we endeavour to raise a weight by means of a le¬ 
ver, we shall find the lever press Jhe hands with the 
same force which we exert upon if to raise the weight. 
Or if we press one scale of a balance, in order to raise 
a weight in the other scale, the pressure against the fin¬ 
ger will be equal to that force with which the other scale 
endeavours to descend. 

When a cannon is fired, the impelling force of the 
powder acts equally on the breech of the gun and on the 
ball, so that if the piece and the ball were of equal 
weight, the piece would recoil with the same velocity as 
that with which the ball issues out of it. But the heav¬ 
ier any body is, the less will its velocity be, provided 
the force which communicates the motion continues the 
same. Therefore, so many times as the cannon and 
carriage are heavier than the ball, just so many times 
will the velocity of the cannon be less than that of the 
ball. 


COMPOUND MOTION. 

1. If two forces act at the same time on any body, and 
in the same direction, the body will move quicker 
than it would by being acted upon by only one of 
the forces, 

2. If a body be acted upon by two equal forces, in ex¬ 
actly opposite directions, it will not be moved from 
its situation, 

3. If a body be acted upon by two unequal forces in ex- 


LAWS OF MOTION. 


47 


uctly contrary directions, it will move in the direc¬ 
tion of the greater force. 

4, If a body be acted upon by two forces, neither in the 
same nor opposite directions, it will not follow 
either of the forces, but move in a line between them. 



The first three of the preceding articles may be 
considered as axioms, being self-evident; the fourth 
may be thus elucidated : Let a force be applied to a 
body at A, in the direction AB, ^ E K B 
which would cause it to move F 
uniformly from A to B in a given ^ 
period of time ; and at the same 
instant, let another force bi* appli¬ 
ed in the direction AC, such as would cause the body 
to move from A to C in the same time which the first 
force would cause it to move from A to B ; by the joint 
action of these forces, the body will describe the diag¬ 
onal AD of a parallelogram,* with an uniform mo¬ 
tion, in the same t ;me in which it would describe one of 
the sides AB or AC Oy one of the forces alone. 

For, suppose a tube equal in length to AB (in which 
a small ball can move freely from A to B) to be moved 
parallel to itself from A to C, describing with its two 
extremities the lines AC and BD, so that the ball may 
move in the tube from A to B in the same time that the 
tube has descended to CD ; it is evident, that when 
the tube AB coincides with the line CD, the ball will 
be at the extremity D of the line, and that it has arri¬ 
ved there in the same time it would have described 
either of the sides AB or AC. The ball will likewise des¬ 
cribe the straight line AD, for by assuming several simi¬ 
lar parallelograms AEGt^^, AKIH, &c. it will appear, 
that while the ball has moved from A to E the tube w ill 
have descended from A to F, consequently, the ball 
will beat G ; and while the ball has moved from A to K, 
the tube will have descended from A to H, and the ball 
will be at I. Now, AGID is a straight line ;f or smaller 
parallelograms that are similar to the whole, and simi¬ 
larly situated, are about the same < iagonal.f 


* A parallelogram is a four-sided figure, having each of the two op¬ 
posite sides equal and parallel, 
t Luclid, Yl. aad 26th. 







4B LAWS OF MOTION. 


b. If a body, by an uniform motion, describe one 
side of a 'paraUelogram, in the same time that it woiitd 
describe the adjacent side by an accelerative force ; this 
body, by the jomt action of these forces, woutd describe 
a curve, terminating in the opposite angte of the paral¬ 
lelogram. 



Let ABDC be a parallelogram, and suppose fhe body 
A <0 be carried through AB by an uni- A 12 k B 
form iorce in the same time that ii 
would be carried through AC by an 
accelerative force, then by the joim 
action of these forces, the body would 
describe a curve AGID. For by the 
preceding illustration, if the spaces AE, 

EK, and KB, be proportional to each other, the spaces 
AF, FH, and HC, will be in the same proportion, and 
the line AGID will be a straight line when the body is 
acted upon by uniform forces ; but in this example, the 
force in the direction AB being uniform, would cause 
the body to move over equal spaces AE, EK, and KB, 
in equal portions of time ; while the accelerative force 
in the direction AC, would cause the body to describe 
spaces AF, FH, and HC, increasing in magnitude in 
equal successive portions of time ; hence, the parallelo¬ 
grams AEGF, AKIH, &c. are not about the same diag¬ 
onal,* therefore, AGID is not a straight line,but a curve. 

6. The curvilinear motions of all the planets arise 
from the uniform projectile motion of bodies in straight 
lines, and the universal power of attraction which 
draws them off from these lines. 

If the body E be projec¬ 
ted along the straight line 
EAF, in free space where it 
meets with no resistance, 
and is not drawn aside by 
any other force, it will (by 
the first law of motion) go on 
for ever in the same direc¬ 
tion, and with the same ve¬ 
locity. For the force which 



* Euclid VI. and 24tl|, 















THE LAWS OF MOTION. 


4^ 


moves it from E to A in a given time, will carry it from 
A to F in a successive and equal portion of lime, and so 
on; there being nothing either to obstruct, or alter its 
motion. But, ii when the projeclile force has carried 
the body to A, another body, as S, begins to attract it, 
with a power duly adjusted and perpendicular to its 
motion at A, it will be drawii from the straight line 
EAF, and revolve about S in the circle* AGOQA. 
When the body E arrives at O, or any other part of its 
orbit, if the small body M, within the sphere of E’s at¬ 
traction, be projected as in the straight line Mn, with a 
force perpendicular to the attraction of E, it will go 
round the body E, in the orbit m, ar;d accompany E in 
its whole course round the body S.—Here S may rep¬ 
resent the sun, E the earth, and M the moon. 

If the earth at A be attracted towards the sun at S, 
so as to fall from A to H by the force of gravity alone, 
in the same time which the projectile force singly would 
have carried it from A. to F ; by the combined action of 
these forces it will describe the curve AG ; and if the ve¬ 
locity with which E is proejcted from be such as it 
would have acquired by falling from A to V (the half of 
AS,) by the force of gravity alone,f it will revolve round 
S in a circle. 

T. If due body revolve round another {as the earth 
round the sunj)so as to vary its distance from the centre 
of motion, the projectile and centripetal forces must 
each be variable, and the path of the revolving body 
will differ from a circle. 


* If any body revolve round another in a circle, the revolving body 
must be projected with a velocity equal to that which it would hare 
acquired by falling through half the radius of the circle towards the 
attracting body. Emerson's Cent, Forces, Prop. ii. 

t A body, by the force of gravity alone, falls 16^*^ feet in the first 
second of time, and acquires a velocity which will carry it uniformly 
through feet in each succeeding second. This is proved experimen¬ 
tally, by writers on mechanics. 


9 



50 


THE LAWS OF MOITOX. 


Thus, if while a prc 
jeclile force would cai 
ry aplaiiel from A lo E 
the sun’s attraction at » 



would bring it from A 


H, (he gravitating pow 


er would be too great 


for the projectile force ; 
the planet, therefore, 


instead of proceeding/^ 


in the circle ABC (as 


in the preceding ar- j) 


tide) would describe 
the curve AO, and ap¬ 


proach nearer to the -y 

sun; SO being less than 

SA,. INow, as the centripetal force, or gravitating power, 
always increases as the square of the planet’s distance 
from the sun diminishes,^ when the planet arrives at O, 
the centripetal force will be increased, which will like- 
wi>se increase the velocity of the planet, and accelerate 
its motion from O to V ; so as to cause it to describe the 
arches OP, PQ,, QR, RD, DT, TV, successively in¬ 
creasing in magnitude, in equal portions of time. The 
motion of the planet being thus accelerated, it gains such 
a centrifugal force, or tendency to fly ofFat V in the line 
VW, as overcomes the sun’s attraction ; this centrifu¬ 
gal or projectile force being too great to allow the plan¬ 
et to approach nearer the sun than it is at V, or even to 
move round the sun in the jpircle t a b c d, &c. it flies 
off in the curve XZM A, with a velocity decreasing as 
graduall v from V to A, as if it had returned through the 
arches YT, TD, DR, ike. to A with the same veloci¬ 
ty which it passed through these arches in its motion 
from A, towards V. At A the planet will have acquir¬ 
ed the same velocity as it had at first, and thus by the 
centrifugal and centripetal forces it will continue to move 
round S. 

Two very natural questions may here be asked ; viz* 
why the action of gravity, if it be too great for the pro- 


^ Newton’s Princip. Book III. Prop* ii* 














THE LAWS OF MOTION". 


51 


jectile force at O, does not draw the planet to (he siin at 
S ? and why the projectile force at V, if it be (oo great 
for the centripetal force, or gravity, at the same point, 
does not carry the planet farther and farlher from the 
sun, till it is beyond the power of his attraction ? 

First. If the projectile torce atA were such as to car¬ 
ry the planet from A to G, double the distance, in the 
same time that it was carried from A to F, it would re¬ 
quire four"^ times as much gravity to retain it in its orbit., 
viz. it must fall through A1 in (he time that the projec¬ 
tile force would carry it from A to G, otherwise it would 
not describe the curve AOP. But an increase of gravity 
gives the planet an increase of velocity, and an increase 
of velocity increases the projectile force ; therefore, the 
tendency of the planet to fly off* from (he curve in a tan¬ 
gent P?n, is greater at P than at O, and greater at 
Q,, than at P, and so on ; hence, while the gravitating 
power increases, the projectile power increases, so that 
the planet cannot be drawn to the sun. 

Secondly. The projectile force is the greatest at, or 
near, the point V, and the gravitating powder is likewise 
the greatest at that point. For if AS be double of VS, 
the centripetal force at V will be four times as great as 
at A, being as the square of the distance from the sun. 
If the projectile force at V be double of what it was at 
A, the space VW, which is the double of AF, will be 
described in the same time that AF was described, and 
the planet will be at X in that time. Now, if (he action 
of gravity had been an exact counterbalance for the pro¬ 
jectile force during the time mentioned, the planet 
would have been at f instead ofX, and it would describe 
the circle t,«, h, c, &c. but the projectile force being 
too powerful for the centripetal force, the planet recedes 
from the sun atS, and ascends in the curve XZM, &;c. 
Yet, it cannot fly off in a tangent in its ascent, because 
its velocity is retarded, and consequently its projectile 
force is diminished, by the action of gravity. Thus, 
when the planet arrives at Z, its tendency to fly off* in a 
tangent Z?i, is just as much retarded, by the action of 
gravity, as its motion was accelerated thereby at Q, 
therefore, it must be retained in its orbit. 


Ferguson’s Astronomy, Art. 153. 



52 


FIGURE OF THE EARTH, &c. 


CHAP. III. 


Of the Figure of the Earth, and its Magniludco 

THE figure of the earth, as composed of land and 
water, is nearly spherical; the proof of this assertion 
will be the principal object of this chapter. The an¬ 
cients held various opinions respecting the figure of the 
earth ; some imagined it to be cylindrical, or in the 
form of a drum: but the general opinion was, that it 
was a vast extended plane, and that the horizon was the 
utmost limits of the earth, and the ocean the bounds of 
the horizon. These opinions were held in the infancy 
of astronomy; and, in the early ages of Christianity, 
some of the fathers went so far as to pronounce it heret¬ 
ical for any person to declare that there was such a 
thing as the antipodes. But by the industry of suc¬ 
ceeding ages, when astronomy and navigation were 
brought to a tolerable degree of perfection, and when it 
was observed that the moon was frequently eclipsed by 
the shadow of the earth, and that such shadow always 
appeared circular on the disc or face of the moon, in 
whatever position the shadow was projected, it necessa¬ 
rily followed, that the earth, which cast the shadow, 
must be spherical; since nothing but a sphere, when 
turned in every position with respect to a luminous bo¬ 
dy, can cast a circular shadow ; likewise all calculations 
of eclipses, and of the places of the planets, are made 
upon supposition that the earth is a sphere, and they all 
answer to the true times when accurately calculated. 
When an eclipse of the moon happens, it is observed 
sooner by those who live eastward than by those who 
live westward ; and, by frequent experience, astrono¬ 
mers have determined that, for every fifteen degrees 
difference of longitude, an eclipse begins so many hours 
sooner in the easternmost place, or later in the western¬ 
most. If the earth were a plane, eclipses would hap¬ 
pen at the same time in all places, nor could one part of 
the world be deprived of the light of the sun, while 
another part enjoyed the benefit of it. The voyages 
of the circumnavigators sufficiently prove that the earth 


FIGURE OF THE EARTH, &c. 


^3 


IS round from west to east. The first who attempted to 
circumnavigate (he globe, was Magellan, a Portuguese, 
who sailed from Seville in Spain, on the 10th of Au¬ 
gust, 1519; he did not live to return, but his ship arriv¬ 
ed at St. Lucar, near Seville, on the Tth of September, 
1522, without altering its direction, except to the north 
or south, as compelled by the winds, or intervening land. 
Since this period, the circumnavigation of the globe 
has been performed at different times by Sir Francis 
Drake, Lord Anson, Captain Cook, 8cc^ The Voyages 
of the circumnavigators have been frequently adduced 
by writers on geography and the globes, to prove that 
the earth is a sphere ; but when we reflect that all the 
circumnavigators sailed westward round the globe, (and 
not northward and southward round it) they might have 
performed the same voyages had the earth been in the 
form of a drum or cylinder; but the earth cannot be in 
the form of a cylinder, for if it were, then the differ¬ 
ence of longitude between any two places would be 
equal to the meridional distance between the same pla¬ 
ces, as on a Mercator’s chart, which is contrary to ob¬ 
servation.—Again, if a ship sail in any part of the 
world, and upon any course whatever ; on her departure 
from the coast, all high towers or mountains gradually 
disappear, and persons on shore may see the masts of 
the ship after the bull is hid by the convexity of the 
water {See P^igure HI. Plate 1 .)—If a vessel sail north¬ 
ward, in north latitude, the people on board may ob¬ 
serve the polar star gradually to increase in altitude 
the farther they go: they may likewise observe new 
stars continually emerging above the horizon which were 
before imperceptible ; and at the same time, those stars 
which appear southward, will continue to diminish in al¬ 
titude, till they become invisible. The contrary phae^ 
nomena will happen if the vessel sail southward ; hence, 
the earth is spherical from north to south, and it has 
already been shown, that it is spherical from east to 
west. 

The arguments already adduced clearly prove the ro¬ 
tundity of the earth, though common experience shows 
us that it is not strictly a geometrical sphere ; for its 
surface is diversified with mountains and valleys : but 
these irregularities no more hinder the earth from being 


5.4 


FIGURE OF THE E/VRTH, 


reckoned spherical, considering its magnitude, than the 
roughness of an orange hinders it from being esteemed 
round.* 

When philosophical and mathematical knowledge ar¬ 
rived at a still greater degree of perfection, there seemed 
to be a very sufficient reason for the philosophers of 
the last age, to consider the earth not truly spherical, but 
rather in the form of a spheroid.f This notion first 
arose from observations on pendulum clocks,J which 
being fitted to beat seconds in the latitudes of Paris and 
London, were found to move slower as they approached 
the equator, and at,’or near, the equator, they were o- 
bliged to be shortened about -Jof an inch, to agree with 
(he times of the stars passing the meridian. This dif- 


* Our largest clobes are in general 18 inches in diameter. The diam¬ 
eter of the earth is about 7964 miles. Chimboraco, one of tlie Andes 
mountains, the highest in the world, is about •ii0608 feet, or nearly 4 
miles high. 17ie radius of the earth is S982 miles, and that of an 18 
inch globe 9 inches. Now, by the rule of three, 398‘2m : 3982m-{-4 
: : 9 in. : 9009, fi-om which, deduct the radius of the artificial globe, 

the remainder .009 =i ~tt7 an inch, nearly, is the elevation of 
the Andes on an 18 inch globe, which is less than a grain of sand. 

t A spheroid is a figure formed by a revolution of an ellipsis about 
its axis, and an ellipsis is a curv^e-lined figure in geometry, formed by 
cutting a cone or cylinder obliquely: but its nature will be more clear¬ 
ly comprehended, by the learner, from the following description ; 

Let TR (in Plate IV Figure V.) be tlie transverse diameter, or 
longer axis of the ellipsis, and CO the conjugate diameter, or shorter 
axis. With the distance TD or DR in your compasses, and C as a cen¬ 
tre, describe the arch Ff; the points F, f, will be the two foci of the 
ellipsis. Take a thread of the length of the transverse axis TR, and 
fasten its ends with pins in F and f, then stretch the thread Fif and it 
will reach to I in the curve, then by moving a pencil round with the 
thread, and keeping it always stretched, it will trace out the ellipsis 
TCRO. If this ellipsis be made to revolve on its longer axis TR. it 
will generate an oblong spheroid, or Cassini’s figure of the earth ; but 
if it be supposed to revolve on its shorter axis CO, it will form an ob¬ 
late spheroid, or Sir Isaac Newton’s figure of the earth.—The orbits or 
paths of all the planets are ellip.se.s, and the sun is situated in one of 
the foci of the earth’s orbit, as will be observed farther on.—The points 
F, f, are called foci, or burning points; because, if a ray of light is¬ 
suing from the point F meet the curve in the point I, it will be reflect¬ 
ed back into the focus f- For lines drawn from the two foci of an ellipsis 
to any point in the curve, make equal angles with a tangent to the 
curve at that point; and by the laws of optics, the angle of incidence 
is equal to the angle of reflection. Robertson’s Conic Sections, Boole 
III. Scholium to Prop. ix. 

$ Philosophical Transactions, No. 386. 



FIGURE OF THE EARTH, &<?. 


55 


ference appearing to Ilujgens* and Sir Isaac Newton, 
to be a much greater quantity than could arise from the 
alteration by heat only, they separately discovered that 
the earth was flatted at the poles.—By the revolution of 
the earth on its axis (admitting it to be a sphere) the 
centrifugal force at the equator would be greater than the 
centrifugal force in the latitude of London or Paris, be¬ 
cause a larger circle is described by the equator, in the 
same time ; but as the centrifugal force, (or tendency 
which a body has to recede from the centre) increases, 
the action of gravity necessarily diminishes; and where 
the action of gravity is less, the vibrations of pendu¬ 
lums of equal lengths become slower; hence, supposing 
the earth to be a sphere, we have two causes why a 
pendulum should move slower at the equator than at 
London or Paris, viz. the action of heat which dilates 
all metals, and the diminution of gravity. But these 
two causes combined,.would not, according to Sir Isaac 
Newton, produce so great a difference as -Jth of an 
inch in the length of a pendulum, he therefore supposed 
the earth to assume the same figure that a homogeneous 
fluid would acquire by revolving on an axis, viz. the figure 
of an oblate spheroid, and found that the “ diameter of 
the earth at the equator, is to its diameter from pole to 
pole, as 230 to 229.Notwithstanding the deductions 
of Sir Isaac Newton, on the strictest mathematical prin- 


* A celebrateH tnathematician, born at the Hague in Holland, in 1629, 
t ^lotte’s translation of Newton’s Principia, Book III. Page 24.‘3. 
Calling the equatorial dianieter of the earth 7964 English miles, the 
polar diameter will be 7929.—For as 2.So : 229 : : 7964 : 7929 mile®, 
the polar axis. Hence, the polar axis is shorter than the equatorial 
diameter by S5 miles, and the earth is higher at the equator than at the 
poles by 17^ miles, a difference imperceptible on the largest globe.<r 
that are made.—Suppose a globe to be 18 inches in diameter at the 
equator, then 2.S0 : 229 : : 18 : irli f flie polar diameter : the dif¬ 
ference of the diameters is inch, half diffeience is ^ 

of an inch, the flatnessof an 18 inch globe at each pole, which is les» 
than the 2Sd part of an inch, or not much thicker than the paper and 
paste, a quantity not to be discovered by the appearance ; and on 
smaller globes the difference would be considerably less. Hence, the 
learner should be informed, that though the earth be not strictly a 
globe, it cannot be represented by any other figure lyliich will give so 
exact an i<lea of its shape; and a lecturer who informs his hearers 
that it is in the shape of a turuip, or an orange, gives a very falie idea 
of its true figure. 



FIGURE OF THE EARTH, &c. 


3i6 

ciples, many of the philosophers in France, the princi¬ 
pal of whom was Cassini, asserted that the earth was an 
oblong spheroiii, the polar diameter being the longer ; 
and as these different opinions were supposed to retard 
the general progress of science in France, the king re¬ 
solved that the affair should be determined by actual 
admeasurment at his own expense. Accordingly, about 
the year I7ti5, two companies of the most able mathe¬ 
maticians of that nation were appointed : the one to 
measure the degree of a meridian as near to the equa¬ 
tor as possible, and the other company to perform a like 
operation as near the pole as could be conveniently at¬ 
tempted. The results of these admeasurements con¬ 
tradicted the assertions of Cassini, and of J. Bernoulli, 
(a celebrated methematician of Basil in Switzerland, 
who warmly espoused his cause) and confirmed the cal¬ 
culations of Sir Isaac NewTon.—In the year 1756, the 
Royal Academy of Sciences of Paris, appointed eight 
astronomers to measure the length of a degree betweert 
Paris and Amiens; the result of their admeasurement 
gave 57069 toises for the length of a degree. 

The utility of finding the length of a degree in order 
to determine the magnitude and figure of the earth, may" 
be rendered familiar to a learner thus; suppose I find 
the latitude of London to be 51A° north, and travel due 
north till I find the latitude of a place to be 52^° north, 
I shall then have travelled a degree, and the distance 
between the two places, accurately measured, will be 
the length of a degree; now if the earth be a correct 
sphere, the length of a degree on a meridian, or a great 
circle, w'ill be equal all over the world, after proper al¬ 
lowances are made for elevated ground, &c. the length 
of a degree multiplied by S60 will give the circumfe¬ 
rence of the earth, and hence its diameter, &c. will be 
easily found: but, if the earth be any other figure than 
that of a sphere, the length of a degree on the same 
meridian will be different in different latitudes, and if 
the figure of the earth resemble an oblate spheroid, the 
lengths of a degree will increase as the latitudes in¬ 
crease. The English translation of Maupertiiis* figure 
of the earth, concludes with these words : “ The degree 
of the meridian which cuts the polar circle being lon¬ 
ger than a degree of the meridian in France, the earih 


FIGURE OF THE EARTH, &c. 


57 


is a spheroid flatted towards the poles.^^ See page 163 
of the Ivork» For the longer a degree is, I he greater 
must be the circle of which it is a part; and the greater 
the circle is, the less is its curvature. 

The first person who measured the length of a degree 
with any appearance of accuracy, was Mr. Richard Nor¬ 
wood ; by measuring the distance between London and 
York, he found the length of a degree to be 367196 En¬ 
glish feet, or 69^ English miles ; hence, supposing the 
earth to be a spliere, its circumference will be *25020 
miles, and its diameter 7964* miles ; but if the length 
of a degree, at a medium, be 57069 toises, the circum¬ 
ference of the earth will be 24873 English miles, its 
diameter 7917 miles, and the length of a degree 69.jlg. 
miles.f 

Conclusion. Notwithstanding all the admeasure¬ 
ments that have hitherto been made, it has never been 
demonstrated, in a satisfactory manner, (bat the earth is 
strictly a spheroid ; indeed, from observations made in 
different parts of the earth, it appears that its figure is 
by no means that of a regular spheroid, nor that of any 
other known regular mathematical figure ; and the only 
certain conclusion, that can be drawn from the works of 
the several gentlemen employed to measure the earih, 
is, that the earth is something more flat at the poles than 
at the equator. —The course of a ship, considering the 


* 5280 feet make a mile, therefore, 367196 divided hy give 
69^ miles nearly, which multiplied by 360 produces 25020 miles, the 
circumference of the earth, but the circumference of a circle is to its 
diameter as 22 to 7, or more nearly as 355 to Il3 ; hence, 355 : 113 : : 
25020 miles ; 7964 miles, the diameter of the earth. \gain 6 French 
feet make t toise, therefore, 57069 toises are equal to .S424t4 French 
feet; but 107 French feet are equal to 114 Englij^h feet; hence, 107 
F f. • 114 E, f, : : 3424 F. f. : 364814 English feet, which, divided 
by .5280 the feet in a mile, gives 69.09 miles, the length of a degree by 
the French admea.surement. Or. 3424H, multiplied by .360, produces 
123 69040 French feet the circumference of the earth, and 107 t <14 
: : 123269040: 13^3.3.3.369 English feet, equal to 24873.74 miles, the 
circumference of the earth, and 355 : 113 : ; 24873.74 : 7917 miles, 
the diameter of the earth 

t The length of a degree in lat, 51® 9' N. is 364950 feet = 69.12 
English miles. Trigonometrical Survey of England and Wales, yol, 
II part II. page 113. IVIr Swanberg, a Swedish mathematician, 
found the length of a degree to be 57196.159 toises = 365627.782 
glish feet s=; 69.^47 miles. 



/>8 MOTION OF THE EARTH, &c. 

earth a spheroid, is so near to what it would be on a 
sphere, (hat (he mariner may safely trust (o (he rules 
of globular sailing,* even though his course and dis¬ 
tance were much more certain than it is possible for 
them (o be. For which, and similar reasons, mathema¬ 
ticians content themselves with considering the earth as 
a sphere in all practical sciences, and hence the artifi¬ 
cial globes are made perfectly spherical, as the best rep¬ 
resentation of the figure of the earth. 


CHAP. IV. 

Of the Diurnal and Annual Motion of the Earth, 

THE motion of the earth was denied in the early 
ages of the world, yet as soon as astronomical knowl¬ 
edge began to be more attended to, its motion received 
the assent of (he learned, and of such as dared to think 
differently from the multitude, or were not apprehen¬ 
sive of ecclesiastical censure.—The astronomers of the 
last and present age have produced such a variety of 
strong and forcible arguments in favour of the motion 
of the earth, as must effectually gain the assent of eve¬ 
ry impartial inquirer.—Among the many reasons for the 
motion of the earth, it will be sufficient to point out the 
following: 

1. Of the Diurnal Motion of the Earth. 

The earth is a globe of 7964 miles in diameter (as has 
been shown in Chap. Ill ) and by revolving on its axis 
every 24f hours from west to east, it causes an apparent 
diurnal motion of all the heavenly bodies from east to 
west.—We need only look at the sun, or stars, to be 


* Rr>()ertson’s Navie:ation. Book VIII. Art. 14.'3. 
t That is, the time from the sun^s being on the meridian of any 
place, to the time of its returning to the same meridian the next day ; 
but the earth forms a complete revolution on its axis in 23 hours 5$ 
piiinutes4 seconds; see definition61,page 13. 



DIURNAL MOTION OF THE EARTH. 


59 


convinced, lhat either the earth, which is no more than 
a point* when compared with the heavens, revolves on 
its axis in a certain time, or else the sun, stars, &c. re¬ 
volve round the earth in nearly the same time. Let us 
suppose, tor instance, that the sun revolves round the 
earth in 24 hours, and that the earth has no diurnal mo¬ 
tion.—Now, it is a known principle in the laws of motion, 
that if any body revolve round another as its centre, 
it is necessary that the central body be always in the 
plane in which the revolving body moves, whatever 
curve it describes ;f therefore, if the sun move round 
the earth in a day, its diurnal path must always des¬ 
cribe a circle which will divide the earth into two equal 
hemispheres. But this never happens except on two 
days in the year, viz. at the time of the equinoxes, 
when the sun rises exactly in the east, and sets exactly 
in the west ; for, in our summer, the sun rises to the 
north of the east, and sets to the north of the west; and, 
therefore, its diurnal path divides the globe into two 
unequal parts; consequently, the sun does not move 
round the earth. To render this more intelligible to a 
young student, let a pin, of some inches in length, be 
fixed perpendicular upon an horizontal plane, and ob¬ 
serve the shadow that the top of it describes on any 
day of the year ; this shadow will always be a curve, 
except at the time of the equinoxes ; hence, the earth 
is never in the sun’s apparent diurnal orbit but then ; 
for if the top of the pin kept all the time in the plane of 
the sun’s apparent diurnal orbit, the shadow described 
would be a straight line,J because it would fall in the in¬ 
tersection of two planes ;§ therefore, the sun has no 
diurnal motion round the earth ; consequently, the 
earth has a diurnal motion on its axis. 

It is no argument against the earth’s diurnal motion 
that we do not feel it ; a person in the cabin of a ship, 
on smooth water, cannot perceive the ship’s motion when 
it turns gently and uniformly round ;|] neither does the 


♦ Dr. Keill, Lect. 26. 
t Emerson’s Astronomy, page 11. 
f Emerson’s Dialling, Prop. II. p. 9th. 

i It is demonstrate*! in Euclid, Prop. III. Book XI. that if twp 
planes intersect each other, their common section is a straight line. 

H Ferguson’s Astronomy, Art. 119. 



^0 DIURNAL MOTION OF THE EARTH. 

motion of the earth cause bodies to fall from its surface ; 
for all bodies, of whatever matter they are composed, 
are drawn to the earth by the power of its central at¬ 
traction which, laying hold of them according to 
their densities, or quantities of matter, without regard 
to their magnitudes, constitutes what we call weight. 

The phenomena of the apparent diurnal motion of the 
sun may be explained by the motion of the earth ; thus, 
let IFGH (plate [. figure v.) represent the earth, S the 
sun, and the circle DSBC the apparent concavity of 
the heavens. Let the earth revolve on its axis from I 
towards G (viz. from west to east.) Suppose a specta¬ 
tor 'o be at 1, the sun, which is at an immense distance, 
and enlightens half the globe at once, will appear to be 
rising. As the earth moves round, the spectator is car¬ 
ried towards F, and the sun seems to increase in height: 
when he has arrived at F, the sun is at the highest. As 
the earth continues to turn round, the spectator is car¬ 
ried from F towards G, and the altitude of the sun 
keeps continually diminishing ; when he has arrived at 
G, the sun is setting. During the time the spectator has 
been carried from I to G, the sun has appeared to move 
the contrary way. Hence, it is evident, that w^hile the 
spectator is carried through the illuminated half of the 
earth, it is day-light; at the middle point F, it is noon ; 
also, while he is carried through the dark hemisphere, 
it is night; and at H it is midnight. Thus, the vicissi¬ 
tude of day and night evidently appears by the rotation 
of the earth about its axis: what has been said of the 
sun is equally applicable to the moon, or any star plac¬ 
ed at S ; therefore, all the celestial bodies seem to rise 
and set by turns, according to their various situations. 
The spectator at I, F, G, H, will always have his feet 
towards the centre of the earth, and the sky above his 
head, whatever position the earth may have : agreeably 
to the laws of gravitation or attraction. Thus an inhab¬ 
itant at a will be the most powerfully attracted towards 
his antipodes 6, because there is the greatest mass of 
earth under bis feet in that direction ; for the same rea¬ 
son b wilFbe the most attracted towards a, m towards n, 


* Newton^s Principia, Book III. Prop. vji. 



ANNUAL MOTION OF THE EARTH. 


61 


and n towards m, &c. hence, it appears that every body 
on ihe surface of the earth is ailnacted towards its cen¬ 
tre, or rather, towards the antipodes of that body, for 
the whole earth is the attracting mass, and not some un¬ 
known substance placed in the centre of the earth. 
There is no such thing as an upper and under side of 
the earth : suppose a to be an inhabitant of Nattkin in 
China, b will be an inhabitant of South America, near 
Buenos Ayres, each having the earth under his feet and 
the sky above his head ; also, if n be an inhabitant a 
little, east of Quito in South America, on the equator^ 
m will be an inhabitant upon the equator in the Inland of 
Sumatra, and in the course of 12 hours n will have the 
same position asm, by the revolution of the earth. 

2. Of the Annual Motion of the Earth. 

The diurnal revolution of the earth on its axis being 
proved, the annual motion round the sun will be readily 
admitted; for, either the earth moves round the sun in a 
year, or else the sun moves round the earth : now, by 
the laws of centripetal force, if (wo bodies revolve a- 
bouteach other, they revolve round their common cen¬ 
tre of gravity ;* and it is evident that if the two bodies 
be of equal magnitude and density, the centre of gravi¬ 
ty will be equidistant from each body ; but, if they be 
of different magnitudes, the centre of gravity will be 
nearest to the larger body ; if the earth, therefore, re¬ 
main in the same situation while the sun revolves round 
it, its magnitude must be vastly greater than that of the 
sun ; for it is contrary to the laws of nature for a heavy 
body to revolve round a light one as its centre of mo¬ 
tion : but from observations on the dimensionsf and dis¬ 
tances of the sun and planets, it appears that the sun so 


* The centre of gravity of two bodies is a point, on which, if they 
were both supported by a line joining their centres, they would rest in 
equilibrium 

t The apparent diameters of the planets are found by a micrometer^ 
placed in the focus of a telescope, or. the apparent diameter of the sun 
maybe measured by means of the projection of his image into a dark 
room, through a circular aperture. From {he.se apparent diameters, 
and the respective distances from the earth, the real diameters of the 
sun and planets may be determined. 



62 


ANNUA.L MOTION OF THE E4RTH. 


greatly exceeds, not only the earth, but the planets. In 
magnitude, that the common centre of gravity of the 
whole is almost constantly within the body of the sun, 
so that the sun’s motion round the common centre of 
gravity of the earth and the planets is not perceptible 
by ordinary observers. Not only the earth, therefore, 
but the planets, move round the sun. 

It is also evident, that the motion of the earth in its 
orbit is from west to east; for if the sun be observed to 
rise with any fixed star which is near the ecliptic, it will, 
in the course of a few days, appear to the eastward of 
that star. And in the space of a ^ ear it will arrive at 
the same star again. 

The earth is computed to be 95 millions of miles from 
the sun,* and performs its revolutions round him, des¬ 
cribing an elliptical orbit, or path,f in 365 days 5 hours 
48 minutes and 48 seconds, from any equinox, or solstice, 


* That part of the heavens in which the sun or a planet would ap¬ 
pear, if viewed from the surface of the earth, is called its apparent 
place; and the point in which it would be seen at the same instant 
from the centre of the earth, is called its true place. The difference 
between the true and apparent place is called the. parallax. In Plate 
IV. Fig.vi. let O be the centre of the earth, P the place of an observ¬ 
er on its surface, and Sthe sun or a planet in the heavens; now, to an 
observer at O, the sun would appear at a, and to an observer at P, it 
would appear at 6; the arch ab. or the angle a s b, which is equal to 
the angle PSO, is called the horizontal parallax. Mr. Short, in vol. 
52, part ii. of the Philosophical transactions, has determined the hor¬ 
izontal parallax of the sun to be 8".65, at its mean distance from the 
earth. Hence, by trigonometry, 

As logarithm leal sine of 8".65, or angle PSO, 5.6219140. 

Is to one semi-diameter of the earth PO, 0 0000000 

As radius, sine of 90 degrees or sine of OPS, 10.00000000 

Is to 23882.84 semi diameters. 4 3780860 

Now, if we take the diameter of the earth T970 miles, as Mr. ^hort 
has done, the semi-diameter .3935, multiplied by 23882 84, gives 
95173117 miles, the distance of the earth frimi the sun if the diam¬ 
eter of the earth be taken 7964 miles, the distance will be 95101468 
miles; if it be taken 7917 miles (see the chapter of the Figure of the 
earth) the distance will be 94540222 miles. In a case of such uncer¬ 
tainty, where a very small error in the parallax will produce an aston- 
ishitiff difference in the conc'usion of the process, and win re an error 
in the diameter of the earth will also affect the operation, we may rest 
contented with estimating the distance of the earth from the sun at 95 
millions of miles. 

t Th,e idea that the earth moved in an elliptical orbit was first con¬ 
ceived by Kepler, an eminent German astronomer, and demonsltaleti 
by Sir Isaac Newton. See the Principia, Book III. Prop. xiii. 



annual motion of the earth. 


,63 


to the same again ; it travels at the rate of upwards of 
68,000 miles per hour."^ Besides this motion, which is 
common to every inhabitant on the earth, the inhabi¬ 
tants at the equator are carried 1042f miles every hour 
by the diurnal revolution of the earth on its axis, while 
those in the parallel of London are carried only about 
644 miles per hour. The axis of the earth makes an 
angle of 23*^ 28' with a perpendicular to the plane of its 
orbit, and keeps always the same oblique direction 
throughout its annual course ;J hence, it follows, that, 
during one part of its course, the north pole is turned 
towards the sun, and, during another part of its course^ 
the south pole is turned towards it in the same propor¬ 
tion ; which is the cause of the different seasons, as 
spring, summer, autumn, and winter. The orbit of the 
earth being elliptical, the earth must at some times ap¬ 
proach nearer to the sun than at others, and will of 
course take more time in moving through one part of its 
path than through another. Astronomers have observ¬ 
ed, that the earth is more rapid in the winter half of its 
orbit than in the summer, by about seven days : (see 
the note to the 6th Geographical Theorem, p. 40 ;) but, 
although in the winter we are nearer to the sun than in 
the summer, yet, in that season, it seems farthest from 
us, and the weather is more cold and inclement : 
the simple account of which phenomenon is, that the 
sun’s rays falling more perpendicularly on us in sum¬ 
mer, augment the heat of the weather ; so, being trans- 


* The earth's distance from the sun is 95 millions of miles, the mean 
diameter of its orbit is therefore 190 millions of miles; and the circum¬ 
ference of a circle is three times the diameter and one-seventh wjore ; 
or the circumference is to the diameter as 355 to 11S more nearly ; 
hence. 1 IS : 355 :: 190 000,000: 596902654 the circumference of the or¬ 
bit ; but this circunjference is described in S65 days 5 hours 48 minutes 
48 seconds, or S65 days 6 hours nearly, or 8766 hours ; hence 8766 h.: 
596902654 ra. : : Ih.: 68092 miles per hour the inhabitants of the earth 
are carried by its annual revolution. 

t These distances are found by multiplying the number of miles con¬ 
tained in a degree in any parallel of latitude by 15; thus, the circum¬ 
ference of the earth at the equator is 360® X 69^ m. and in the latitude 
of London it is equal to S60‘’ X 42.65- and ^ h.; 360® X 1 h.: 

1042^ m.; or 1 :15 X 69^ : : 1 : 1042^ m 

f This is not strictly true, though the variation, called the nutation 
of the earth’s axis, is scarcely perceptible in tW 9 or three years. Kei%. 
Lect. viii. 



64 


ANNUAL MOTION OF THF EARTtf. 


mitted more obliquely on our parallel of laiilude during 
the winter, the cold is increased and rendered moie in¬ 
tense. The heat in the torrid zone does not arise Irom 
those parts of the earih being nearer to the sun, but from 
the ra^^s of the sun falling perpendicular upon, and 
darting immediately through the atmosphere. It might 
likewise be expected, that, as we are less distant from 
the sun in the winter than in the summer, it would ap¬ 
pear larger; but the difference of situation is so small 
as to make no sensible alteration in the sun’s apparent 
magnitude. 

The sun is not supposed to be fixed in the centre of 
the earth’s elliptical orbit, but in one of the foci. Let 
S represent the sun, (Plate II. Fig; 3.) and AGFBDE, 
the elliptical orbit of the earth. Then A is called the 
Perihelion, or lower apsis, being the earth’s nearest dis¬ 
tance from the sun ; B is called the Aphelion, or higher 
apsis, being the greatest distance of the earth from 
the sun, and SC the distance between the sun, (in 
the focus) and the centre, is called the eccentricity 
of the earth’s orbit. If from the centre C, there 
be erected upon the axis AB the perpendicular CE 
meeting the orbit in E, and the line SE be drawn, it 
will represent the mean distance of the earth from the 
Bun, being equal to half the axis AB,* consequently, 
SE is 95 millions of miles. 

Though the motion of the earth in its orbit be not 
uniform, yet it is regulated by a certain immutable law, 
from which it never deviates; which is, that a line drawn 
from the centre of the sun to the centre of the earth, 
being carried about with an angular motion, describes 
an ellipticafl area proportional to the time in which that 
area is described,! viz. if the times in which the earth 
moves from A to E, from E to D, and from D to B, be 
equal, then the areas, or spaces, ASE, ESI), and 
DSB, will all be equal. The motion of the earth is 
sometimes quicker and sometimes slower in moving 
through equal parts of its orbit; for, when the earth is 


• It is demonstrated by all writers on conic sections, that a line 
drawn from one end of the conjugate axis of an ellipsis to the focus, is 
equal to half the transverse axis, viz. SE =: FB or C A. 

t This law was discovered by Kepler, and demonstrated by Sir Isaai? 
Newton. See Frincipia, Book 111. Prop. xUi. 



ANNUAL MOTION OF THE EARTH. 


65 


'at A (in the winter) the sun attracts it more strongly, 
and therefore, the motion is quicker than any where 
else; likewise, when it is at B (in the summer) it is 
least affected by the sun’s attraction, and consequently, 
the motion there is slower than in any other part of its 
orbit, for the power of gravity decreases as the square 
of the distance increases besides, it is obvious, from 
the construction of the figure, that, if the space ASE be 
described in the same time with the space BSD, the 
arch AE will be greater than the arch BD. 

The phenomena of the different seasons of the year 
will appear plainly from the following observations. Let 
ABCD (Plate III. Figurel.) represent the plane of the 
earth’s annual orbit, having the sun in the focus F ; and 
let a by an imaginary line passing through fhe centre of 
the earth, be perpendicular to this plane ; and let the 
axis NS, of the earth make an angle of 23° 28' with this 
perpendicular: then if the earth move in the direction 
A, B, C, D, in such a manner that NS may always re¬ 
main parallel to itself, and preserve the same angle with 
a by it will point out the seasons of the year; for, sup¬ 
pose a line to be drawn from the centre of the sun to the 
centre of the earth, it is evident that the sun will be 
vertical to that part of the earth which is cut by this 
line. Now, when the earth is in Libra the sun will 
appear to be in Aries T, the days and nights will be 
equal in both hemispheres, and the season a medium 
between summer and winter ; the line dividing the dark 
and light hemispheres passes through Ihe two poles N and 
S, and consequently, divides all Ihe parallels of latitude, 
as PR, into two equal parts ; hence, the inhabitants of 
the whole face of the earth have their days and nights 
equal, viz. twelve hours each* While the earth moves 
from Libra to Capricorn >?, the north pole N will be¬ 
come more and more enlightened, and the south pole S 
will be gradually involved in darkness, consequently, 
the days in the northern hemisphere will continue to in*- 
crease in length, and in the southern hemisphere they 
will decrease in the same proportion, all the parallels of 
latitude being unequally divided. When the earth has 


# Newton’s Principia, Book III. Prop. ii. 

n 



(36 


ANNUAL MOTION OF THE EARTH. 


arrived at Capricorn , the sun will appear to be in Can" 
cer S , il will be summer to the inhabitants ol the north¬ 
ern hemisphere, and winter to those in the southern: 
the inhabitants at the north pole, and within the arctic 
circle, will have constant da)', and those at the south 
pole, and within the antarctic circle, will have constant 
night. While the earth moves from Capricorn ^5 to 
Aries T, the south pole will become more and more en¬ 
lightened ; consequently, (he days in the southern hem¬ 
isphere will increase in length, and in the northern hem¬ 
isphere they will decrease. When (he earth has arri¬ 
ved at Aries T, the sun will appear to be in Libra 
and the days and nights will again be equal all over the 
guiTace of (he earth. Again, as the earth moves from 
Ar.es T towards Cancer 25, the light will gradually 
leave the north pole and proceed to the south : when 
the earth has arrived at Cancer 25, it will be summer to 
the inhabitants in the southern hemisphere, and winter 
to those in the northern : the inhabitants of the south 
pole (if any) will have continual day, (hose at the north 
pole constant night. Lastlv, while the earth moves 
from Cancer 25 to Capricorn V5, the sun will appear to 
move from Capricorn ^5 to Cancer 25, and the days in 
the northern hemisphere will be increasing, while those 
in the southern will be diminishing in length; and while 
the earth moves from Capricorn >5 to Cancer 25, the sun 
will appear to move from Cancer 25 to Capricorn VJ, 
the days in the northern hemisphere will then be de¬ 
creasing, and those in the southern hemisphere increas¬ 
ing. In all situations of the earth, the equator will be 
divided into two equal parts,, consequently the days and 
nights at the equator are always equal. Thus (he dif¬ 
ferent seasons are clearly accounted for, by the inclina¬ 
tion of the axis of (he earth to the plane of its orbit,* 
combined with the parallel motion of that axis. 


* In atl.tition to tliese observations, the author farther illustrates the 
seasons of the year by an orrery ; and soinetitnes by a brass wire eup» 
ported on two studs of different heights, correspondent to the diameter 
of the wire circle, and the obliquity of the ecliptic; as in I'erguson’s 
Astromony, chap. x. But, as this last method does not so clearly show 
the obliquity of the axis of the earth to the plane of its orbit: take a 
board of any convenient dimensions, suppose two feet across, on which 
describe a circle, or an ellipsis differing little from a circle, draw a diam- 



ORIGIN OF SPRINGS AND RIVERS, &c 


67 


CHAP. V. 

Of the Origin of Springs and RiverSy and of the Salt¬ 
ness of the Sea* 

VARIOUS opinions have been held by ancienf, as 
well ah mudern philosophers, respecting the origin of 
springs and rivers; but the true cause is now pret»y well 
ascertained. It is well known that the heal of the sun 
draws vast quantities of vapour from the sea, which be¬ 
ing carried by the wind to all parts ot the globe, and 
being converted by the cold into rain and dew, it falls 
down upon the earth ; part of it runs down into the low er 
places, forming rivulets, part serves for the purposes of 
vegetation, and the rest descends into hollow caverns 
within the earth, which breaking out by the sides of the 
hills forms little springs; many of these springs running 
into the valleys increase the brooks or rivulets, and sev¬ 
eral of these meeting together make a river. 

Dr. Halley* says, the vapours that are raised copi¬ 
ously from the sea, and carried by the winds to the 
ridges of the mountains, are conveyed to their tops by 
the current of air; where the water being presently 
precipitated, enters the crannies of the mountains, down 
which it glides into the caverns, till it meets with a 
stratum of earth or stone,- of a nature sufficiently solid to 
sustain it. When this reservoir is filled, the superfluous 


eter OFO (Plate III. Figure 1) and parallel to this diameter let sev¬ 
eral lines e/be drawn, then bore several holes perpendicularly down in 
the points e e, &c. of the circumference of the circle ; take two pieces of 
wire crossing each other in an angle of 23® 28'; as «g, and n/ of which 
a g the perpendicular wire is the longer, and connect them by a straight 
wire t /; then placing a small globe on the point n, and a light in the 
centre of the circle, of the same height as the centre of the little globe; 
let the point g in the longer wire be fixed successively in the holes, e, 
e, &c. in the circumference of the circle, so that th^' base e f of the wire 
may rest on the lines e/in the plane of the earth’s orbit, the seasons of 
the year will be agreeably and accurately illustrated If the little 
globe be placerl upon the point a, instead of the point n, and the same 
method be observed in moving the wires round the orbit, there will 
be no diversity of seasons. The diurnal revolution of the earth may 
be shown by moving the globe round the wire n /, as an axis, with the 
finger 

* Philosophical Transactions, No. 192, 



6n 


ORIGIN OF SPRINGS AND RIVERS, AND 


water, following the direction of the stratum, runs over 
at the lowest place, and in its passagemeets perhaps with 
other little streams, which have a similar origin: these 
gradually descend till they meet with an aperture at the 
side, or foot of the mountain, through which they es¬ 
cape and form a spring, or the source of a brook or riv¬ 
ulet. Several brooks or rivulets, uniting their streams 
form small rivers, and these again being joined by other 
small rivers, and united in one common channel, form 
such streams as the Rhine, Rhone, Danube, &c. 

Several springs yield always the.same quantity of 
water, equally when the least rain or vapour is afforded, 
as when rain falls in the greatest quantities; and as the 
fall of rain, snow, &c. is inconstant or variable, we have 
here a constant effect produced from an inconstant 
cause, which is an unphilosophical conclusion. Some 
naturalists, therefore, have recourse to the sea, and de¬ 
rive the origin of several springs immediately from 
thence, by supposing a subterraneous circulation of per¬ 
colated waters from the fountains of the deep. 

That the sun exhales as much vapour as is suflScient 
for rain is past dispute, having been several times proved 
by actual experiments. Dr. Halley"^ determined by 
experiment and calculationf, that in a summer’s day, 
there may be raised in vapours from the Mediterranean 
5280 millions of tuns of water, and yet the Mediterra¬ 
nean does not receive from all its rivers above 1827 mil¬ 
lions of tuns in a day, which is little more than a third 
part of what is exhausted by vapoursj; and from the 
river Thames, twenty millions three hundred thousand 
tuns may be raised in one day in a similar manner.—In 
the Old Continent there are about 430 rivers which fall 
directly into the ocean, or into the Mediterranean and 
Black Seas, and in the New Continent, scarcely 180 
rivers are known, which fall directly into the sea: but 


* Dr Halley was an eminent mathematician, astronomer, and phi¬ 
losopher, born in London in the year 1656. 
t Philosophical Fransactions, No. 212. 

X As evaporation cannot carry off fixed salts, it would appear that 
if the above calculation be accurate, the Mediterranean would be more 
salt than the Ocean, but it must be remembered that a current sets con¬ 
stantly out of the Atlantic Ocean into the Mediterraneaji. 



OP THE SALTNESS OF THE SEA. 69^ 

in this number, only the greatest rivers are comprehend¬ 
ed All these rivers carry to the sea a great quantity 
of mineral and saline particles, which they wash from 
the different soils through which they pass, and the par¬ 
ticles of salt, which are easily dissolved, are conveyed 
to the sea by the water. Dr. Halle}^ imagines that the 
saltness of the sea proceeds from the salts of the earth 
only, which rivers convey thither, and that it was orig¬ 
inally fresh. So that its saltness will continue to in¬ 
crease : for, the vapours which are exhaled from the 
seas are entirely fresh, or devoid of saline particles. 
Others imagine that there is a great number of rocks of 
salt at the bottom of the sea, and from these rocks it ac¬ 
quires its saltness. Some writers again, have imagined 
that the sea was created salt that it might not corrupt; 
but it may well be supposed that the sea is preserved 
from corruption by the agitations of the wind, and from 
the flux and reflux of the tide, as much as by the salt it 
contains ; for when sea water is kept in a barrel it cor¬ 
rupts in a few days. The Honourable Mr. Boylef re¬ 
lates that a mariner becalmed for thirteen days, found, at 
the end of that time, the sea so infected, that if the calm 
had continued, the greatest part of his people on board 
would have perished.—The sea is nearly equally salt 
throughout, under the equinoctial line and atihe Cape 
of Good Hope, though there are some places on the Mo¬ 
zambique coast where it is salter than elsewhere. It is 
also asserted, that it is not quite so salt under the arctic 
circle as in some other latitudes, J this probably may pro¬ 
ceed from the great quantity of snow, and the great riv¬ 
ers which fall into those seas : to which we may add, 
that the sun does not draw such quantities of fresh wa'^ 
ter, or vapours, from those seas as in hot countries. 

It is worthy of remark, that all lakes from which rivers 
derive their origin, or which fall into the course of riv- 


♦ BuffonN Natural History. 

t A ynuuj^er son of tbe Earl of Cork, and one of the most celebra¬ 
ted philosophers in Europe, born at Lismore. in the county of Water- 
lord, See his Treatise on the Saltness of the Sea, published in 

1674 

f Tn a Sysiem of Chemistryhy Dr. Thomson, of Edinburgh, Tol. IV. 
fourth edition^ page -41, it is stated, that the ocean contains most salt 
between 10° and south latitude, and that the proportion of salt is 
the least in latitude 57® north. 



70 


ORIGIN OF SPRINGS AND RIVERS, &l. 


ers, are not saline and almost all those, on the conlra^ 
rj, which receive rivers, without other rivers issuing 
from them, are saline ; this seems to favour Dr. Hal¬ 
ley’s opinion respecting the sail ness of the sea, for evap¬ 
oration cannot carry off fixed salts, and consecpienlly 
those salts which rivers carry into the sea remain there. 
It is assertedf to be the peculiar property of sea-wafer, 
that when it is absolutely salt it never freezes ; and that 
the islands or rocks of ice which float in the sea near the 
poles, are originally frozen in the rivers, and carried 
thence to the sea by the tide ; where they continue to 
accumulate by the great quantities of snow and sleet 
which fall in those seas. According to this opinion, 
great quantities of ice can be produced only from great 
quantities of fresh water, or from large rivers, and as 
large rivers can only flow from large tracts of land, it 
would appear that there must be immense tracts of land 
near the south pole, for the Antarctic Ocean abounds 
with fields or mountains of ice, as well as the Arctic 
Ocean; but our circumnavigators have traversed the 
southern Ocean to upwards of seventy degrees south 
latitude, without discovering any land. With respect 
to the freezing of salt water, we have several instances 
of the Baltic,J and other seas being frozen over, when 
the ice on the surface could never proceed from rivers. 
It is true that the sailors frequently take large pieces of 
the rocks of ice, and thaw them for the use of the ship’s 
company, and always find the water fresh ; but it does 
not follow from this that the ice is formed in the rivers. 
As fresh water is only extracted from sea-water by the 
heat of the sun, and carried into the atmosphere : may 
not the fresh, without the saline particles of sea-water, be 
converted into ice by extreme cold ?— 


* BufFon’s Natural History, Chap. II. 
t Emerson’s Geography, page 64 

I The Baltic Sea is not so salt as the Ocean, and the proportion of 
salt is increased by a west wind, and still more by a north-west wind : 
a proof that not only the saltness of the Baltic is derived from the 
ocean, but that storms have a much greater effect upon the waters of 
the ocean than has been supposed.—Dr. Thomson's Chemistrij^ Vol IV. 
page 141.—The Baltic ‘^ea has little or no tides, and a current runs con¬ 
stantly through the Sound into the Cattegate sea. 



FLUX AND REFLUX OF THE TIDES. 


71 


CHAP. VI. 

Of the Flux and Reflux of the Tides. 

A TIDE is that motion of the water in the seas and 
rivers, by which they are found to rise and fall in a regu¬ 
lar succession ; and this flowing and ebbing is caused by 
the attraction of the sun and moon.'’^ 

Suppose the earth to be entirely covered by a fluid, 
as A, B, C, D, Q, N, {Plate III. Figure 2.) and the ac¬ 
tion of the sun and moon to have no eftect upon it, then 
it is evident that all the particles, being equally attract¬ 
ed towards the centre O of the earth, would form an ex¬ 
act spherical surface ; except, that by the revolution of 
the earth on its axis NS, the attraction from B towards 
O, and from Q, towards O would be a little diminished 
by the centrifugal force. Let the moon atM now exert 
her influence upon the water; then, because the power of 
attraction diminishes as the square of the distance in¬ 
creases, those parts will be the most attracted which are 
the nearest to the moon, and their tendency towards O 
will be diminished; the waters at Z, B, and C, will, 
therefore, rise, and at Z, which is nearest to the moon, 
they will be the highest; but when the waters in the 
zenith Z are elevated, those in the nadir N are likewise 
elevated in a similar manner; this is known from experi¬ 
ence, for we have high water when the moon is in our 
nadir, as well as when she is in’our zenith; we, therefore 
conclude, that when the moon is in our zenith, our anti¬ 
podes have high water; the truth of this, as well as 
every other phienornenon respecting the tides, will be 
discussed in the following theorems. 

Theorem 1.1 The parts of the earth directly under 
the moon, or where the moon is in the Zenith, as at Z, 


* This was known to the ancients: Pliny expressly says, that the 
cause cf the ebh and flow is in the sun, which attracts the waters of the 
ocean, and that they also rise in proportion to the proximity of the 
moon to the earth. Dr. Hutlon^s Math. Dictionary, word Tides. 

t A theorem is a propo.sition which admits of proof, or demonstra¬ 
tion, from definitions clearly understood, and from the known general 
properties of the subject under consideration. 



72 


FLUX AND REFLUX OF THE TIDES. 


(Plate in. Fig. 3.) and those places which are dia¬ 
metrically opposite to the former, or under the ISa- 
dir, as at N, will have high water at the same time. 

Because the power of gravity decreases as the square 
of the distance increases : the waters at A, B, Z, C, 1), 
on the side of the earth next the moon M, will be more 
attracted by the moon than the central parts O of the 
earth, and the central parts will be more attracted thaa 
the surface N on the opposite side of the earth; there¬ 
fore, the distance between the centre of the earth and 
the surface of the water, under the zenith and nadir, 
will be increased. For, let three bodies Z, O, and N, 
be equally attracted by M ; then it is evident the> will 
ail move equally fast towards M, and their mutual dis¬ 
tances from each other will continue the same; but if 
the bodies be unequally attracted by 31, that body w hich 
is the most attracted will move the fastest, and its dis¬ 
tance from the other bodies will be increased. Now, 
by the law of gravitation, 31 will attract Z more strongly 
than it does O, by which the distance between Z and 
O will be increased. In like manner O being more 
strongly attracted than N, the distance between O and 
N will be increased; suppose now a number of bodies, 
A, B, Z, C, D, F, N, E, placed round O, to be attract¬ 
ed by 31, the parts Z and N will have their distances 
from O increased ; while the parts A and D, being rjear^* 
ly at the same distance from M as O is, will not recede 
from each other, but will rather approach nearer to O by 
the oblique attraction of 31. Hence, if the whole earth 
were composed of bodies similar to A, B, Z, C, D, F, 
N, E, and to be similarly attracted by 31, the section 
of the earth, formed by a plane passing through the 
moon and the earth’s centre, would be a %ure resemb¬ 
ling an ellipsis, having its longer axis ZN directed to¬ 
wards the moon; and its shorter axis AD in the horizon. 
The figure of the earth therefore would be an oblong 
spheroid, having its longer axis directed to the moon, 
consequently, it will be high water in the zenith and na¬ 
dir, at the same time ; and as the earth turns round its 
axis from the moon to the moon again in about 24 hours 
and 48 minutes, there will be two tides of flood and twQ 
of ebb in that time, agreeably to experience? 


FLUX AND REFLUX OF THE TIDES, 73 

According to the foregoing explanation of the ebbing 
and flowing of the sea, every part of the earth is gravi¬ 
tating towards the moon ; but as the earth revolves round 
the sun, every part of it gravitates towards the sun like¬ 
wise ; it may be asked, how is this possible at the time of 
full moon, when the moon is at m and the sun at S; has 
the earth a tendency to fall contrary ways at the same 
time ? This is a very natural question, but it must be 
considered, that it is not the centre of the earth"that,de- 
scribes the annual orbit round the sun, but the common 
centre of gravity ot the earth and moon together; and 
that whilst the earth is moving round the sun, it also de¬ 
scribes a cirele round that centre of gravity, about w hich 
it revolves as many times as the moon revolves round 
the earth in a year."^ The earth is, therefore, constantly 
falling towards the moon, from a tangent to the circle 
which it describes round the common centre of gravity 
of the earth and moon. Let M represent the moon 
(Plate IH. Figured.) TW a part of the moon’s orbit, 
and as the earth is supposed to contain about 40 times 
the quantity of matter which is contained in the moon, 
the common centre of gravity from the centre of the 
earth towards the moon, will be considerably less than 
the earth’s diameter :f let this common centre of gravity 
be represented by C. Then white the moon goes round 
her orbit, the centre of the earth describes the circle 


^ Ferguson’s Astronomy, article ^98. 

t rhe common centre of gravity of two bo<lics is found thus, as the 
sum of the weights, or quantities of matter in the two bodies is to their 
distance from each other, so is the weight of the less body to the dis¬ 
tance of the greater from the centre of gravity. Now, if the quantity 
of matter in the moon be represented by 1, that in the earth by 40, 
and the distance of the earth from the moon be estimated at 240,000 
miles, then 40 1 : 240,000 :: 1 : .>853 miles, the distance of the centre 

of the eai'tb from the common centre of gravity Mr. A, Walker, in the 
11th lectiii’e of his Familiar Philosophy, ingeniously accounts for its 
being high-water in the zenith and nadir at the same time, in the fol¬ 
lowing manner : “ The parts of the earth that are farthest from the 

moon, will have a swifter motion round the centre of gravity than the 
other parts; thus, the side n will describe the circle n V Y, while the 
side m will only describe (he small circle wr s, round the centre o( 
gravity C. Now, as every thing in motion always endeavours to go 
forward in a straight line the water at n having a tendency to go off in 
the line nq w ill in a degree o'^ercome power of gravity, and swell 
int<< a heap of protuberance, as represented in the figure, and occasion 
a tide opposite to that caused by the attraction of the moon.” 

12 




74 


FLUX ANDHEFLUX OF THE TIDES. 


doe round C, to which circle o ah a tangent: therefore, 
wiien the moon has gone from M to a little past W, the 
earth has moved from o to e ; and in that time has fallen 
towards the moon from the tangent at a to e. This fig¬ 
ure is drawn for the new moon, but the earth will tend 
towards the moon in the same manner during its whole 
revolution round C. 

Theorem II. Those parts of the earth where the moon 
appears in the horizon, or 90 degrees distant from the 
Zenith and Sadir^ as at A and D, (Plate 111. Fig¬ 
ure 3.) will have ebbs or, low water. 

For, as the water under the zenith and nadir rise at 
the same time, the waters in their neighbourhood will 
press towards those places to maintain the equilibrium; 
and to supply the place of these waters, others will 
move the same way, and so on to places of 90 degrees 
distance from the zenith and nadir ; consequently, at A. 
and D, where the moon appears in thej horizon, the wa¬ 
ters will have more liberty to descend towards the cen* 
tre of the earth ; and therefore, in those places they will 
be the lowest. Hence, it plainly appears, that the ocean, 
if it covered the whole surface of the earth, would be a 
spheroid, (as was observed in the foregoing theorem) 
the longer diameter as ZN passing through the place 
where the moon is vertical, and the shorter diameter as 
AD passing through the rational horizon of that place. 
And as the moon apparently* shifts her position from 
east to west in going round the earth every day, the lon¬ 
ger diameter of the spheroid following her motion will 
occasion the two floods and ebbs in about 45 hours and 
48 minutes,! the time which any meridian of the earth 


* The real motion of the moon is from the west towards the east; 
for if '•he be seen near any fixed star on any night, she will be seen 
about degrees to the eastward of that star the next night, and so on. 
Tbe moon goes round her orbit from any fixed star to the same again in 
about TI days 0 hours. Hence, 57 d, 8 h.SGO® ; : 1 d.: 13® Ky 14" .6 
the mean motion of the moon in 24 hours. 

t The mean motion of the moon in 24 hours is IS® 10' 14" ,6 and the 
mean apparent motion of the sun in the same time is 59' 8''.2 {see the- 
note to de.finii)on 6;. pat^e IS) the moon's motion is therefore l2® 11' 6" 
.4 s \ifter than the hpi arent motion of the^un in one day, which, reck- 
i>Jiing 4 minutes to a degree, amounts to 48 minutes 44 seconds of time. 



FLUX AND REFLUX OF THE TIDES. 


75 


takes in revolving from the moon to the moon again ; 
or the time elapsed (at a medium) between the passage 
of the moon over the meridian of any place, to her re¬ 
turn to the same meridian. 

The meridian altitude of the moon at any place is her 
greatest height above the horizon at that place ; hence, 
the greater the moon’s meridian altitude is, the greater 
the tides will be; for they increase from the horizon D 
to the point Z under the zenith: and the greater the 
moon’s meridian depression is below the horizon, the 
greater the tides will be ; for they increase from the ho¬ 
rizon D towards N the point below the nadir, and con¬ 
sequently, as the tides increase from D to N, the tides in 
their antipodes will increase from A to Z. 

Theorem III. The time of high water is not precisely 
at the time of the moon’s coming to the meridian, but 
about an hour after. 

For, the moon acts with some force after*she has pass¬ 
ed the meridian, and by that means adds to the librato- 
ry, or waving motion, which the waters had acquired 
whilst she was on the meridian. 

Theorem IV. The tides are greater than ordinary 
twice every month, vis. at the times of new and full 
moon, and these are called Spring-tides. {PlateIII. 
Figure 3.) 

For, at these times, the actions of both the sun and 
moon concur to draw in the same straight line SMZON, 
and, therefore, the sea must be more elevated. In con¬ 
junction, or at the new moon, when the sun is at S, and 
the moon at M, both on the same side of the earth, their 
joint forces conspire to raise the water in the zenith at 
Z, and consequently (according to Theorem I.) at N 
the nadir likewise.* When the sun and moon are in 


♦ Mr. Walker says (Lecture 11th) that at new moon “ The sun’s in¬ 
fluence is added to that of the moon, ami the centre of gravity C (Plate 
II/. Figure 4.) will, therefore, be removed farther from the earth than 
m C, and of course, increase the centrifugal tendency of the tide n: 
hence, both the attracted and centrifugal tides are spring-tides, at that 
time.”—** But spring-tides take place at the full as well as at the change 



76 FLUX AND REFLUX OF THE TIDES. 

opposition, or at the full moon, when (he sun is at S anti 
the moon at m, the earth being between (hem ; while the 
sun raises the water at Z under (he zenith and at N un¬ 
der the nadir, the moon raises the Avater at N under the 
nadir and at Z under the zenith. 

Theorem V. The tides are less than ordinary twice 
every month ; that is about the time of the first and 
last quarters of the moon, and these are called Neap^ 
TIDES. {Plate III. Figure 3.) 

Because, in the quadratures, or when the moon is 90 
degrees from tlie sun, the sun acts in the direction SD, 
and elevates (he water at D and A ; and the moon act¬ 
ing in the .direction MZ or mN, elevates the water at Z 
and N : so that the sun raises the water where (he moon 
depresses it, and depresses the water where the moon 
raises it; consequently, the tides are formed only by (he 


of the nioon. Now, it has been premised, that if we had no moon, the 
gun would agitate the ocean in a small degree, and make two tides every 
twenty-four hours, thontjh upon a small scaled 't he moon’s centrifugal 
tide at Z {Plate ITI. Figure 8.) being increased by the sun’s attraction 
at S, will make the protuberatice a spring-tide; and the s?m’s centrifu¬ 
gal tide at N will be reinforced by (he moon’s attraction at m, and make 
the protuberance N a spring-tide ; so spring-tides take place at the full 
as well as change of the moop.'—'Suppose the moon to be taken away 
(Plate HI. Figure k ) the common fcentre of gravity of the earth and 
sun w'ould fall entirely within the body of the sun, round which the 
earth revolves in a year at the rate of about a degree in a day : hence, 
the parts n of (he earth farthest from the sun would have a little more 
tendency to recede from the centre of motion S, than the part^ m which 
are the nearest '•o that if the sun^ere on the meridian of any place 
it would be high water at that place by the sun’s attraction, and it 
would at the same time be high water at the antipodes of that place by 
the centrifugal tendency of n ; consequently, as the earth revolves on 
its axis from noon to noon in 24 hours, there would be two tides ot flood 
and tw o of ebb during that time. If the hnOair?!. C be increased w hen 
the moon i« in conjunction with the sun, so as to cause the point n to 
describe a larger circle than n V Y, and also the point w to describe a 
larger circle than m r s round the centre of gravity C ; wdien the sun is 
in opposition to the moon, the line m C will be diminished, ti will 
therefore describe a smaller circle than nY Y, and m will describe a 
smaller circle than m r s. Hence, it appears, that the centrifugal ten¬ 
dency of n is greater at the new moon than it is at the full moon, and m 
is likewise more stronglv attracted at the same time; the spring-tides 
at the time of conjunction w^ould therefore be considerably greater than 
at the time of opposition, were not the moon’s centrifugal tide at this 
time attracted by the sun, and the sun’s centrifugal tide added to that 
(saused by the moon’s attraction. 



FLUX AND REFLUX OF THE TIDES. 


77 . 


liifterence between the attractive force of the sun and 
moon.— i he waters at Z and N will be more elevated 
than the waters at D and A, because the moon’s attrac¬ 
tive force is four* times that of the sun. 

Theorem VI. The spring-tides do not happen ex¬ 
actly on the day of the change or full moon, nor the 
neap-tides exactly on the days of the quarters, but a 
day or two afterwards. 

When the attractions of the sun and moon have con¬ 
spired together for a considerable time, the motion im¬ 
pressed on the waters will be retained for some time «f- 
ter their attractive forces cease, and consequently, the 
tide will continue to rise. In like manner at the quar¬ 
ters, the tide will be the lowest when the moon’s attrac¬ 
tion has been lessened by the sun’s for several days to¬ 
gether.—If the action of the sun and moon were sudden¬ 
ly to cease, the tides would continue their course for 
some time, like as the waves of the sea continue to be 
agitated after a storm. 

Theorem VII. When the moon is nearest to the earth, 
or in Perigee, the tides increase more than in simi¬ 
lar circumstances at other tmies. 

For the power of attraction increases as the square of 
the distance of the moon from the earth decreases ; con- 


* Rp Isaac Newton, Cor. 3. Prop. XXXVII. Book III. Principia, 
makes the force of the moon to that of the snn, in raising the waters of 
the ocean, as 4.4815 to 1; and in Corel i • of the same proposition, he 
calculates the height of the solar tide to he ^'d'eetO inches 4, the lunar 
tide 9 feet 1 inch and by their joint attraction 11 feet 2 inches; 
when the moon is in Perigee, the joint force of the sun and moon will 
raise the tides upwards of J34 feet.—Sir Isaac Newton’s measures are in 
French feet in the Principia. I have turned them into English feet. 

Mr Emerson, in his Fluxions, Section III. Prob. 25. catcuiates the 
greatest height of the solar tide to be 1 63 feet, the lunar tide. T 28 feet, 
and by their joint attractions 8.91 feet, making the force of the sun to 
that of the moon as 1 to 4 4815. 

Dr. Horsley.’the late Bishop ofSt .\saph estimates the force of the 
moon to that of the sun as 5.0469 to I. 'ee hi** edition of the Principia, 
lib. 3. sect. 3. Prop. XXXVI. and XXXVll. 

Mr. Walker, in Lecture Itth of his Familiar Philosophy, states the 
influence of the sun to be to the influence of the moon to raise the water, 
as 3 is to 10, and their joint force IS. 



7S FLUX AND REFLUX OF THE TIDES. 

sequently, the moon must attract most when she is near¬ 
est to the earth* 

Theorem VIIL The spring tides are greater a short 
time before the vernal tquinoxy and if ter the autum¬ 
nal equinox, vis, about the latter end of March and 
September, than at any other time of the year. {Flale 
ill. Figure 3.) 

Because, the sun and moon will then act upon the 
equator in the direction a f B ; consequently, the 
spheroidal figure of the tides will then revolve round its 
longer axis, and describe a greater circle than at any 
other time of the year ; and, as this great circle is de¬ 
scribed in the same time that a less circle is described, 
the waters will be thrown more forcibly against the 
shores in the former circumstance than in the latter. 

Theorem IX. Lakes are not subject to tides; and 
small inland seaSy such as the Mediterranean and 
Baltic, are little subject to tides. In very high lati¬ 
tudes, north or south, the tides are also inconsider¬ 
able. 

The lakes are so small, that when the moon is vertical 
she attracts every part of them alike. The Mediterra¬ 
nean and Baltic seas have very small elevations, because 
the inlets by which they communicate with the ocean 
are so narrow, that they cannot, in so short a time, re¬ 
ceive or discharge enough to raise or lower their surfa¬ 
ces sensibly. 

Theorem X. The time of the tides happening in par¬ 
ticular places, and likewise their height, may be ve- 
ry dijferent according to the situation of these pla¬ 
ces. 

For, the motion of the tides is propagated swifter in 
the open sea, and slower through narrow channels or 
shallow places; and, being retarded by such impedi¬ 
ments, the tides cannot rise so high. 


FLUX AND REFLUX OF THE TIDES. 79 

General Observations. 

The new and full moon spring-tides rise to different 

heights. 

The morning tides differ generally in their rise from 
the evening tides. 

In winter, the morning tides are highest. 

In summer, the evening tides are highest. 

The tides follow, or flow towards the course of the 
moon, when they meet with no impediment. Thus, the 
tide on the coast of Norway flows to the south, (towards 
the course of the moon) from the North-cape in Nor¬ 
way to the Naze, at the entrance of the Scaggerac, op 
Cattegate Sea, where it meets with the current which 
sets constantly out of the Biltic Sea, and consequently, 
prevents any tide rising in the Scaggerac. The tide 
proceeds to the southward along the east coast of Great 
Britain, supplying the ports successively with high wa¬ 
ter, beginning first on the coast of Scotland. Thus, it is 
high water at Tynemouth Bar at the time of new and 
full moon about three hours after the time of high water 
at Aberdeen ; it is high water at Spurn-head about two 
hours after the time of high water at Tynemouth Bar; 
in an hour more it runs down the Humber, and makes 
high water at Kingston upon Hull; it is about three 
hours running from Spurn-head to Yarmouth Road; 
one hour in running from Yarmouth Road to Yar¬ 
mouth Pier; hours in running from Yarmouth Road 
to Harwich ; hour in passing from Harwich to the 
Nore; from wtience it proceeds up the Thames to 
Gravesend and London. From the Nore, the tide con¬ 
tinues to flow to the southward to the Downs and God¬ 
win Sands, between the north and south Foreland in 
Kent, where it meets the tide which flows out of the En¬ 
glish Channel through the Strait of Dover. 

While the tide, or high water, is thus gliding to the 
southward along the eastern coast of Great Britain, it 
also sets to the southward along the western coasts of 
Scotland and Ireland: but on account of the obstructions 
it meets with by the Western Islands of Scotland, and 
the narrow passage between the north-east of Ireland, 
and the south-west ofScofland, the tide in the Irish sea 
comes round by the south of Ireland through St. George’s 


80 


FLUX AND REFLUX OF THE TIDES. 


Channel, and runs in a norlh-east direction till it meets 
the tide between Scotland and Ireland, at the north west 
part of the Isle of Man. This may be naturally inferred 
from its being high water at Waterford above 3 hours 
before it is high water at Dublin, and it is high water at 
Dundalk Bay and the Isle of Man nearly at the same 
time. That the tide continues its course southward may 
be inferred from its being high water at Ushant, opposite 
to Brest in France, about an hour after the time of high 
water at Cape Clear, on the southern coast of Ireland. 
Between the Lizard Point in Cornwall and the island of 
Ushant, the tide flows eastward, or east north-east, up 
the English Channel, along the coasts of England and 
France, and so on through the strait of Dover till it 
comes to the Godwin Sands or Galloper, where it meets 
the tide on the eastern coast of England, as has been 
observed before. The meeting of these two tides con¬ 
tributes greatly towards sending a powerful tide up the 
river Thames to London; and when (he natural course 
of these two tides has been interrupted by a sudden 
* change of the wind, so as to accelerate the tide which 
it had before retarded, and to drive back that tide which 
had before been driven forward by the wind, this cause 
has been known to produce high water twice in the 
course of three or four hours. The above account of 
the British tides seems to contradict the general theory 
of the motions of the tides, which ought always to followr 
the moon, and flow from east to west: but, to allow the 
tides their full motion, the ocean in which they are pro¬ 
duced ought to extend frorn^east to west at least 90 de¬ 
grees, or 6255 English miles; because, that is the dis¬ 
tance between the places where the water is the most 
raised and depressed by the moon. Hence, it appears 
that it is only in the great oceans that the tide can flow 
regularly from east to west; and, hence, we also see why 
the tides in the Pacific Ocean exceed those in the At¬ 
lantic, and why the tides in the torrid zone, between 
Africa and America, though nearly under the moon, do 
not rise so high as in the temperate zones northward and 
southward, where the ocean is considerably wider. The 
tides in the Atlantic, in the torrid zone, flow from east 
to west till they are stopped by the continent of Ameri¬ 
ca ; there the trade winds likewise continue to blow in 


NATURAL CHANGES OF THE EARTH, &c. 81 

that direction. VA^hen (he action of the moon upon the 
waters has in some degree ceased, the force of the trade 
winds, in a great measure, prevents their return towards 
the AtVican shores. The water thus accumulated* in 
the gulf of Mexico, returns to the Atlantic between the 
Island of Cuba, the Bahama Islands, and East Flori¬ 
da, and forin that remarkable strong current called the 
Gulf of Florida. 


CHAPTER VII. 

Of the Natural Changes of the Earthy caused hy Moun-^ 
tains, Floods, Volcanoes, and Earthquakes, 

THAT there have always been mountains from the 
foundation of the world, is as certain as that there have 
always been rivers, both from reason and revelation ;f 
for they were as necessary before the flood for every 
purpose as they are at present. If the earth were per¬ 
fectly level, (as some of our world-makers have imagin¬ 
ed, though directly contrary to the Scripture) there 
could be no rivers, for water can flow only from a higher 
to a lower place ; and instead of that beautiful variety 
of hills and valleys, verdant fields, forests, &c. which 
serve to display the goodness and beneficence of the 
Deity, a dismal sea would cover the whole face of the 
earth, and render it at best an habitation for aquatic ani¬ 
mals only. 

All mountains and high places continually decrease in 
height. Rivers running near mountains undermine and 
wash a part of them away, and rain falling on their sum- 


* To show that an accumulation of water does take place in the 
gulf of Mexico, a survey was made across the isthmus of Darien, when 
the water on the Atlantic was found to be 14 feet higher than the wa¬ 
ter on the Pacific side. Walker’s Familiar Philosophy, Lecture xi. 

t Four rivers, or rather four branches of one river, are expressly 
mentioned before the flood, viz. Pison, Oihon, Hiddekel, and the Ea- 
plirales. Genesis, chap. ii. And in the 7th chapter of Genesis, at the 
time of the flood, we are told that the fountains of the great deep were 
broken up, the windows of heaven were opened, the waters prevailed 
exceedingly upon the earth, and all the high hills and mountains were 
covered. 


13 



NATURAL CHANGES OF THE EARIH, 


mils washes away (he loose parts, and saps the founda> 
(ions of (he solid parts, so that, in course of time, they 
tumble down. Thus, old buildings on the tops of moun¬ 
tains are observed to have their foundations laid bare by 
the gradual washing away of the earth. In plains and 
valleys we find a contrary effect; the particles of earth 
washed down from the hills, fill up the valleys, and an¬ 
cient houses, built in low places, seem to sink. For the 
same reason, a quantity of mud, slime, sand, earth, &c. 
which is continually washed down from the higher pla¬ 
ces into the rivers, is carried by the stream, and, by de¬ 
grees, choaks up the mouths of rivers, especially when the 
soil through which they run is of a loose and rich quali¬ 
ty. Thus, the water of the river Mississippi, though 
wholesome and well tasted, is so muddy, that a sediment 
of two inches of slime has been found in a half pint tum¬ 
bler of it this river is choaked up at the moulh with 
the mud, trees, &c. which are washed down it by the ra¬ 
pidity of the current. 

A circumstance related by Dr. Plot, in his Natural 
History of Staffordshire, will serve to give an idea of 
the quantity of earth which (he rain washes from moun¬ 
tains, and carries along with it into the valleys. He 
says, that, at eighteen feet deep in the earth, a great 
number of pieces of money, coined in the reign of Ed¬ 
ward V, (viz. two hundred years before his time,) have 
been found ; so that this ground which is boggy, has in¬ 
creased near a foot in eleven years, or an inch and one- 
twelfth every year. 

The highest mountains in the world are the Andes, in 
South America, which extendnear 4300 miles in length, 
from the province of Quito to the strait of Magellan ; 
the highest, called Chimborazo, is said to be 20608 feet, 
or nearly four miles, above the level of the sea; 2400 
feet of which, from the summit, are always covered with 
snow. From experiments made with a barometerf on 


* Morse’s American Geography. 

t The quicksilver in a barometer falls about one-tenth of an inch eve¬ 
ry S2 yards of height; so that, if the quicksilverdescend three-tenths of 
an inch, in ascending a hill, the perpendicular height of that hill will be 
96 yards. This method is liable to error. See the causes which affect 
the accuracy of Barometrical experiments, in the Edinburgh Philo¬ 
sophical Transactions, by Mr. Playfair; and in Keith’s Trigonometry, 
s'econd edition, paj^e 91. 



by mountains, IT.OODS, Sec. 


the mountain Cotopaxi, another part of the Andes, it ap¬ 
peared that its summit was elevated 62o2 yards, or up¬ 
wards of 3^ miles above the surface of the sea. There 
is a mountain in the island of Sumatra, tailed Ophir by 
the Europeans, the summit of which is 13842 feet high; 
the Peak of Teneriffe, in the island of that name, is said 
to be 13265 feet, or upwards of2T miles high. Mont 
Blanc, the highest mountain in Europe, is 15304 feet a- 
bove the level of (he sea. These irregularities, although 
very considerable with respect to us, are nothing when 
compared with (he magnitude of the globe: thus, if an 
inch were divided into one hundred and eleven parts, the 
elevation of Chlmbora 90 , the highest of the Andes, on a 
globe of eighteen inches in diameter, would be represent¬ 
ed by one* of these parts. 

Hence the earth, which appears to be crossed by the 
enormous height of mountains, and cut by the valleys 
and the great depth of the sea, is nevertheless, wUh re¬ 
spect to its magnitude, only very slightly furrowed with 
irregularities, so trifling indeed, as to cause no difterence 
in its figure. 

Having, in some measure, accounted for the descend¬ 
ing of the earth from the hills, and filling up the valleys, 
stopping the mouths of rivers, &c. which are gradual, and 
much the same in all ages, (he more remarkable changes 
may be reduced to two general causes, floods and earth¬ 
quakes. 

The real or fabulous deluges mentioned by the an¬ 
cients, may be reduced to six or seven ; and, though 
some authors have endeavoured to represent them ail as 
imperfect traditions of the universal deluge, recorded in 
the sacred writings, the abbe Mann,-f from whom the 
following observations are extracted, does not doubt but 
that they refer to various real and distinct events of the 
kind. 

1. The submersion of the Atlantis of Plato, probably 
was the real subsidence of a great island, stretching from 
the Canaries to the Azores, of which those groups of 
small islands are the relics. 


* See the note (Chap III. page 54) of the figure of the Earth, 
t Vide Nouveaux Memoires de I’Academie Imperiale Sc Iloyale deg 
Sciences et des Belles Lettres, de Brussels, tome premier, 1788, 



84 


NATURAL CHANGES OF THE EARTH, 


2. The deluge in the lime of Cadmus* and Dardanus', 
placed by the best chronologists in the year i)efore 
Christ, 1477, is said by Diodorus Siculus to haVe inim* 
dated Samothrace and the Asiatic shores of the Euxine 
sea. 

3. The deluge of Deucalion, which the Ariindelian 
raarbles,f or the Parian Chronicles, tix at 1529 years be¬ 
fore Christ, overwhelmed Thessaly. 

4. The deluge of Ogyges, placed by Acusilaus in the 
year answering to ir96 before Christ, laid waste Attica 
and Boeotia. With the poetical and fabulous accounts 
of Deucalion’s flood, are mingled several circumstances 
of the universal deluge ; but the best writers attest the 
Jocality and distinctness both of the flood of Deucalion 
and Ogyges. 

5. Diodorus Siculus, after Manetho, mentions a flood 
which inundated all Egypt in the reign of Osiris; but, in 
the relations of this event, are several circumstances re¬ 
sembling the history of Noah’s flood. 

6. The account given by Berosus, the Chaldean, of an 
universal deluge in the reign of Xisuthrus, evidently re¬ 
lates to the same event with the flood of Noah. 

7. The Persian Guebres, the Brainins, Chinese, and 
Americans, have also their traditions of an universal de¬ 
luge. The account of the deluge in the Koran has this 
remarkable circumstance, that tfle waters which cover¬ 
ed the earth, are represented as proceeding from the 
boiling over of the cauldron, J or oven, Tannour, within 
the bowels of the earth ; and that, when the waters sub¬ 
sided, they were swallowed up again by the earth. 

The abbe next gives a summary of the Scripture ac- 
fjount of Noah’s flood, and points out very clearly, that 


* Tbe. ancient names which occur here may all be found in Lem- 
priere’s Classical Dictionary. 

t Ancient stones, whereon is inscribed a chronicle of the city of 
Athens, enjE^raven in capital letters, in the island of Paros, one of tho 
Cyclades, 264 years before Christ. They take their name from Thomas, 
Earl of Arundel,'who procured them from the East. They were pre¬ 
sented to the University of Oxford in the year 1667, by the Hon. Hen¬ 
ry Howard, afterwards duke of Norfolk, grandson to the first collector 
of them. 

:j: This circumstance is mentioned here, because it agrees with Mr. 
Whitehurst’s theory of the earth ; he supposes the flood was occasioned 
|)y the expansive force of fire generated at the centre of the earth. 

i » • ’ 




BY MOUNTAINS, FLOODS, &c. 


85 


part of the wafers came from the atmosphere, and part 
from under ground, agreeably to the lllh verse of the 
viith chapter of Genesis. 

Earthquakes are another great cause of the changes 
made in the earth. From history, we have innumerable 
instances of the dreadful and various effects of these ter¬ 
rible phenomena. Pliny has not only recorded many 
extraordinary phenomena which happened in his own 
time, but has likewise borrowed many others from the 
writings of more ancient nations. 

1. A city of the Lacedemonians was destroyed by an 
earthquake, and its ruins wholly buried by the moun¬ 
tain Taygetus falling down upon them.* 

2. In the books of the Tuscan Learning, an earthquake 
is recorded, which happened within the territory of Mo¬ 
dena, when L. Martins and S. Julius were consuls, 
which repeatedly dashed two hills against each other ; 
with this conflict all the villages and many cattle were 
destroyed. 

3. The greatest earthquake in the memory of man, 
was that which happened during the reign of Tiberius 
Caesar, when twelve cities of Asia were laid level in one 
pight.-f 

4. The eruption of Vesuvius, in the year 79,J over¬ 
whelmed the two famous cities of Herculaneum^ and 
Pompeii, by a shower of stones, cinders, ashes, sand, 
&c. and totally covered them many feet deep, as the 
people were sitting in the theatre- The former of these 
cities was situated about four miles from the crater, and 
the latter about six. 

By the violence of this eruption, ashes were carried 
over the Mediterranean sea into Africa, Egypt, and 
Syria; and at Rome they darkened the air on a sudden, 
so as to hide the face of the sun.|l 


* Pliny^s Natural History, chap. 79. 

t Pliny, chap. 84. 

f Pliny lost his life by this eruption, from too eager a curiosity in 
viewing the flames. 

$ This city was discovered in the year 1736, eighty feet below the 
surface of the earth ; and some of the streets of Pompeii, &c. hare since 
been discov'ered. 

II Burnet’s Sacred History, page 85, vol. ii. 



BG natural changes of the earth. 

5.. In the year 1533, large pieces of rock were thrown 
to the distance of fifteen miles, by the volcano Cotopaxi, 
in Peru.^ 

6. On the 29th of September, 1535, previous to an 
eruption near Puzzoli, which formed a new mountain of 
three miles in circumference, and upwards of 1200 feet 
perpendicidar height, the earth frequently shook, and 
the plain lying between the lake Averno, mount Barba- 
ro, and the sea, was raised a little; at the same time 
the sea, which was near the plain, retired two hundred 
paces from the shore.f 

7. in the year 1538, a subterraneous fire burst open 
the earth near Puzzoli, and threw such a vast quantity of 
a^es and pumice stones, mixed with water, as covered 
the whole country, and thus formed anew mountain, not 
less than three miles in circumference, and near a quar¬ 
ter of a mile perpendicular height. Some of the ashes 
of this volcano reached the vale of Diana, and some parts 
of Calabria, which are more than one hundred and fifty 
miles from Puzzoli.J 

8. In the year 1538, the famous town called St. Eu- 
phemia, in Calabria Ulterior, situated at the side of the 
bay under the jurisdiction of the knights of Malta, was 
totally swallowed up with its inhabitants, and nothing 
appeared but a fetid lake in the place of it.§ 

9. A mountain in Java, not far from the town of Pa- 
nacura, in the year 1586, was shattered to ^pieces by a 
violent eruption of glowing sulphur, (though it had never 
burnt before,) whereby ten thousand people perished in 
the underland fields.|1 

10. In the year 1600, an earthquake happened at Ar- 
quepa, in Peru, accompanied with an eruption of sand, 
ashes, &c. which continued during a space of twenty 
days, from a volcano breaking forth : the ashes falling, 
in many places, above a yard thick, and in some places 
more than two, and where least, above a quarter of a 
yard deep, which buried the corn grounds of maize and 


* Ulloa’s Voyaeje to Peru, vol. i. p. 324. 
t Sir William Hamilton’s Obser\^ations on Vesuvius. 
t Ibid. p. 128. 
i Dr. Hooke’s Post. p. 306. 

{| Varenius’s Geography, vol. i. p. 150. 



BY MOUNTAINS, FLOODC, &c. 


87 


wheat. The boughs of trees were broken, and the cat¬ 
tle died for want of pasture ; for the sand and ashes, thus 
erupted, covered the fields ninety miles one way, and 
one hundred and twenty another way. During this erup¬ 
tion, mighty thunders and lightnings were heard and seen 
ninety miles round Arquepa, and it was so dark whilst 
the showers of ashes and sand lasted, that the inhabi¬ 
tants were obliged to burn candles at mid-day.^ 

11. On the 16th of June, 1628, there was so terrible 
an earthquake in the island of St. Michael, one of the 
Azores, that the sea near it opened, and in one place, 
where it was one hundred and sixty fathoms deep, threw 
up an island; which in fifteen days, was three leagues 
long, a league and a half broad, and 360 feet above the 
water.f 

12. In the year 1631, vast quantities of boiling water 
flowed from the crater of Vesuvius, previous to an erup¬ 
tion of fire ; the violence of the flood swept away sever¬ 
al towns and villages, and some thousands of inhabi¬ 
tants. J 

13. In the year 1632, rocks were thrown to the dis¬ 
tance of three miles from Vesuvius.§ 

14. In the year 1646, many of those vast mountains, 
the Andes,II were quite swallowed up and lost.TF 

15. In the year 1692, a great part of Port Royal, in 
Jamaica, was sunk by an earthquake, and remains cov¬ 
ered with water several fathoms deep ; some mountains 
along the rivers were joined together, and a plantation 
was removed half a mile from the place where it former¬ 
ly stood.** 

16. On the 11th of January, 1693, a great'earth¬ 
quake happened in Sicily, and chiefly about Catania ; 
the violent shaking of the earth threatened the whole is¬ 
land with entire desolation. The earth opened in sev¬ 
eral places in very long clefts, some three or four inches 


* Dr. Hooke’s Post. p. SOA. 

t Sir W. Hamilton’s Observations on Vesuvius and Ailtna, p. 159. 

X Ibid. 

t Baddam’s Abridg Phil. Trans, vol. ii. p. 417. 

II M. Condamine represents these mountains and the Appenines as 
Qhaias of volcanoes. See his Tour through Italy, 1755. 

IT Dr. Hooke’s Post. p. SOS. 

■f* Lovvthorp’s Abridg. Phil. Trans, vol. ii. p. 41/. 



NATURAL CHANGES OF THE EARTH, 


aa 

broad, others like great gulfs. Not less than 59,969 per¬ 
sons were destroyed by the falling of houses in different 
parts of Sicily.* 

IT. In the year 1699, seven hills were sunk by an 
earthquake in the island of Java, near the head of the 
great Batavian river, and nine more were also sunk near 
the Tangarang river. Between the Batavian and Tan- 
garang rivers, the land was rent and divided asitnder, 
with great clefts more than a foot wide.f 

18. On the 20th of November, 1720, a subterraneous 
fire burst out of the sea near Tercera, one of the Azores, 
which threw up such a vast quantity of stones, &c. 
in the space of thirty days, as formed an island about 
two leagues in diameter, and nearly circular. Prodi¬ 
gious quantities of pumice stone, and half-broiled fish, 
were found floating on the sea for many leagues round 
the island.J 

19. In the year 1746, Calloa, a considerable garrison 
town and sea port in Peru, containing 5000 inhabitants, 
was violently shaken by an earthquake on the 28th of 
October ; and the people had no sooner began to recov¬ 
er from the terror occasioned by the dreadful convul¬ 
sions, than the sea rolled in upon them in mountainous 
waves, and destroyed the whole town. The elevation 
of this extraordinary tide was such, as conveyed ships of 
burden over the garrison walls, the towers, and the town. 
The town was razed to the ground, and so completely 
covered with sand, gravel, &c. that not a vestige of it 
remained. § 

20. Previous to an eruption of Vesuvius, the earth 
trembles, and subterraneous explosions are heard; 
the sea likewise retires from the adjacent shore, till the 
mountain is burst open, then returns with impetuosity, 
and overflows its usual boundary. These undulations 
of the sea are not peculiar to Vesuvius ; the earthquake, 
which destroyed Lisbon on the first of November, 1755, 
was preceded by a rumbling noise, which increased to 
such a degree as to equal the explosion of the loudest 


* Lowthorp’s Abridg. Phil. Trans, vol. ii. p- 408, 409. 
t Ibid. vol. ii. p. 419. 

t Eatnes’ Abridg. Phil. Trans, vol. vi. partii. p.203. 
f Osborne’s Relation of Earthquakes. 



BY MOUNTAINS, FLOODS, &c. 


89 


cannon. About an hour after these shocks, the sea was 
observed from the high grounds to come rushing towards 
the city like a torrent, though against wind and tide ; it 
rose forty feet higher than was ever known, and sudden¬ 
ly subsided. At Rotterdam, the branches or chande¬ 
liers in a church were observed to oscillate like a pen¬ 
dulum ; and we are told that it is no uncommon thing to 
see the surface of the earth undulate as the waves of the 
sea, at the time of these dreadful convulsions of nature.^ 

21. The last eruption of Vesuvius, happened in July, 
1794, being the most violent and destructive of any 
mentioned in history, except those in 79 and 1631. The 
lava covered, and totally destroyed 5000 acres of rich 
vineyards and cultivated lands, and overwhelmed the 
town of Torre-del-Greco ; the inhabitants, amounting to 
18,000, fortunately es^caped; and the town is now re¬ 
building on the lava that covers their former habitations. 
By this eruption the top of the mountain fell in, and the 
mouth of Vesuvius is now little short of two miles in cir¬ 
cumference. 

Earthquakes are generally supposed to be caused by 
nitrous and sulphureous vapours, inclosed in the bowels 
of the earth, which by some accident take fire where 
there is little or no vent. These vapours may take fire 
by fermentation,! or by the accidental falling of rocks 
and stones in hollow places of the earth, and striking a- 
gainst each other. When the matters which form sub¬ 
terraneous fires ferment, heat, and inflame, the fire 
makes an effort on every side, and, if it does not find a 
natural vent, it raises the earth and forms a passage by 
throwing it up, producing a volcano. If the quantity 
of substances which takes fire be not considerable, an 
earthquake may ensue without a volcano being formed. 
The air produced and rarefied by the subterraneous 
fire, may also find small vents by which it may escape, 
and in this case there will only be a shock, without any 


* See the Phil. Trans, respecting the earthquake on the first of No¬ 
vember, 1755, vol. xlix. part 1. 

t An equal quantity of sulphur and the filings of iron (about 10 or 
15lb.) worked into a paste with water, and buried in the ground, will 
hurst into a flame in eight or ten hours, and cause the earth round it to 
tremble. 


14 



3^ ^ATUllAIi CHAMOES OF THE EARTH, &c. 

eruption or volcano. Again, all inflammable substances, 
capable of explosion, produce, by inflammation, a great 
quantity of air and vapour, and such air will necessarily 
be in a state of very great rarefaction: when it is com¬ 
pressed in a small space, like that of a cavern, it will not 
shake the earth immediately above, but will search for 
passages in order to make its escape, and will proceed 
through the several interstices between the different 
strata, or through any channel or cavern which may af¬ 
ford it a passage. This subterraneous air or vapour 
will produce in its passage a noise and motion propor¬ 
tionable to its force and the resistance it meets with : 
these effects will continue till it finds a vent, perhaps in 
the sea, or till it has diminished its force by expansion. 

Mr. Whitehurst imagines, that fire and water are the 
principal agents employed in these dreadful operations 
of nature and that the undulations of the sea and 
earth, and the oscillations of pendulous bodies, are phe¬ 
nomena which arise from the expansive force of steam, 
generated in the bowels of the earth by means of subter¬ 
raneous fires ; the force of steam being twenty-eight 
times greater than that of gunpowder, viz. as 14,000 is 
to SOO.f 

It is evident, that there is a great quantity of steam 
generated in the bowels of the earth, especially in the 
neighbourhood of volcanoes, from the frequent eruptions 
of boiling water and steam, in various partsofthe world. 
Dr. Uno Von Troil, in his Letters on Iceland, has re¬ 
corded many curious instances. “ One sees here,’’ says 
he, within the circumference of half a mile, or three 
English miles, forty or fifty boiling springs together : in 
some, the water is perfectly clear, in others, thick and 
clayey, in some, where it passes through a fine ochre, it 
is tinged red as scarlet; and in others, where it flows over 
a paler clay, it is while as milk.” The water spouts up 
from some of these springs continually, from others only 
at intervals. The aperture, through which the water 
rose ill the largest spring, was nineteen feet in diameter. 


* M. Dolomieu seems to be of the same opinion, 
t Inquiry into the Original State and Formation of the Earth, chap, 
xi, page 112. 



theories of the E4RTH, kc. 


91 


and the greatest height to which it threw a column of 
water was ninety-two feet. Previous to this eruption, 
a subterraneous noise was frequently heard like the ex¬ 
plosion of cannon ; and several stones which were thrown 
into the aperture during the eruption, returned with (he 
spouting water. 


CHAP. VIII. 

Hypotheses of the Antediluvian world, and the cause of 
JSoaJds Flood, 

“ Go, teach eternal Wisdom how to rule, 

Then drop into thyself, and '.e a fool.” pope. 

THERE have been various opinions, conjectures, 
and hypotheses, respecting the original formation of the 
earth. The writers of these hypotheses, not satisfied 
with the Mosaical account of the creation, though they 
had no other certain foundation to build upon, thought 
themselves at liberty to model the earth according to 
the dictates of their own imaginations. Hence, we have 
had as great a variety of theoretical systems as writers, 
and these so contradictory and discordant to each other, 
that, instead of throwing light upon the subject, they 
have, if possible, involved it in greater obscurity.* 

1. Dr. BURNET’S THEORY.! 

Dr. Burnet supposes that the earth was originally a 


* The object of all the writers is to prove that Noah’s flood might 
have been produced by natural causes, without the immediate interposi¬ 
tion of the Almighty. Each of these hypotheses contains much useful 
information, blended in the common mass of fiction and conjecture. 
The author of this work has been induced to draw up, in as small a 
Compass as possible, a general outline of each of these hypotheses; and 
to show occasionally, in short notes, the insufficiency of any of them to 
account for the preservation of mankind, and the different animals, with¬ 
out the particular protection of the Divine Power. 

t See Dr. Keill’s examination and confutation of this theory. Dr. 
Goldsmith, in his Animated Nature, calls it a theory alike distinguish¬ 
ed for the elegance of its language, and the shallowness of its argu¬ 
ments. 



92 


THEORIES OF THE EARTH. 


fluid massor chaos, composed of various substances, dif¬ 
fering both in density and figure : those which were the 
most dense sunk to the centre, and formed there a hard 
solid body; those which were specifically lighter re¬ 
mained next above ; and the waters, which were still 
lighter, covered the w hole surface of the earth. The air 
and other ethereal fluids, which were lighter than wa¬ 
ter, floated above the waters, and totally surrounded the 
globe. Between the waters, however, and the circum¬ 
ambient air, was formed a coat of oily and unctuous 
matter, lighter than water. The air at first was very 
impure, and must necessarily have carried up with it 
many of those particles with which it was once blended ; 
however, it soon began to purify itself, and deposit 
those particles upon the oily crust above mentioned, 
which soon uniting tor.^ther, the earth and oil became the 
crust of vegetable earth, wdth which the whole globe is 
now covered. 

At this time the earth was smooth, regular, and uni¬ 
form, without mountains, and without a sea. In order 
to form rivers, he supposes the heat of the sun cracked 
the outward crust of the earth, and so raised vapours 
from the great abyss below. There was no diversity or 
alteration “of the seasons of the year, but a perpetual 
summer; the heat of the sun therefore, acting continu¬ 
ally upon the earth, made the cracks or fissures wider 
and wider, and, as it reached the waters in the abyss, it 
began to rarefy them, and generate steam or vapour. 

These vapours being pent in by the exterior earth, 
pressed with violence against the crust, and broke it in¬ 
to millions of fragments these fragments falling into 
the abyss, drew down with them vast quantities of air, 


* During these violent convulsions in nature, how were Noah and 
the animals preserved without the immediate interposition of Provi¬ 
dence ? The only animals that could stand any chance of escaping des¬ 
truction would be the fishes; and how they could exist in the great a- 
byss below, without air, is not easy to conceive. There was no wa¬ 
ter on the surface of the earth till the excessive heat of the sun 
cracked the oily and vegetable crust: now, if the animals and 
Adam, &c. were created before this crust was cracked, how did they 
exist without water ? In the Mosaical account of the creation, in the 
first chapter of Genesis, we find the wisdom and goodness of God dis¬ 
played, by providing subsistence for his creatures before they were 
created. ‘ 



THEORIES OF THE EARTH. 


93 


and by dashing against each other, and breaking into 
small parts by the repeated violence of the shock, they at 
length left between them large cavities, containing noth¬ 
ing but air. These cavities naturally offered a bed to 
receive the influent waters ; and, in proportion as they 
filled, the face of the earth became once more visible. 

The higher parts of its surface now became the tops 
of mountains, and were the first that appeared; the 
plains next made their appearance ; and at length the 
whole globe was freed from the waters, except the pla¬ 
ces in the lowest stations ; so that the ocean and seas are 
still apart of the ancient abyss. Islands and rocks are 
fragments of the earth’s former crust; continents are 
larger masses of its broken substance; and all the in¬ 
equalities which are to be found on the surface of the 
present earth, are effects of the confusion into which 
both the earth and water were at that lime thrown. 

‘ Dr. WOODWARD’S THEORY.* 

Dr. Woodward begins with asserting, that all earthly 
substances are disposed in beds of various natures, ly¬ 
ing horizontally one over the other, similar to the coats 
of an onion ; that they are replete with shells and oth¬ 
er productions of the sea, these shells being found in 
the deepest cavities, and on the tops of the highest 
mountains. 

From these observations, which are warranted by ex¬ 
perience, he proceeds to observe, that these shells and 
extraneous fossils are not productions of the earth, but 
are all actual remains of those animals which they are 
known to resemble; that all the strata, or beds of earth, 
lie underneath each other in the order of their specific 
gravity,! and that they are disposed as if they had 
been left there by subsiding waters ; consequently, all 


* See Dr. Arbuthnot’s examination of this theory, and comparison 
thereof with Steno’s hypothesis. 

t This is by no means true, for we find layers of stone over the 
lightest soils, and the softest earth under the hardest bodies. The spe¬ 
cific gravity of water is less than that of earth; and, therefore, 
would, if this hypothesis were true, constantly overflow the earth; 
and, instead of a terraqueous, we should have an aqueous surface, a fit 
habitation for nothing but fishes ! 



94 


THEORIES OF THE EARTH. 


the substances of which the earth was composed were 
originally in a state of dissolution. This dissolution he 
supposes to have taken place at the flood : but, being 
aware of an objection, that the shells, &c. supposed to 
have been deposited at the flood, are not dissolved, he 
exempts them from the solvent power of the waters, and 
endeavours to show, that they have a stronger cohesion 
than minerals ; and, that while even the hardest rocks 
are dissolved, bones and shells may remain entire. 

S. Mr. WHIST0N»S THEORY.* 

Mr. Whiston supposes the earth was originally a 
comet ; and considers the Mosaic account of the crea¬ 
tion as commencing at the time when the Creator plac¬ 
ed this comet in a more regular manner, and made it a 
planet in the solar system. Before that time he sup¬ 
poses it to have been a globe without beauty or pro¬ 
portion ; a world in disorder, subject to alf the vicissi¬ 
tudes that comets endure, and alternately exposed to 
the extremes of heat and cold. These alterations of heat 
and cold, continually melting and freezing the surface 
of the earth, he supposed to have produced, to a cer¬ 
tain depth, a chaos surrounding the solid contents of the 
earth. The surrounding chaos he describes as a dense 
though fluid atmosphere, composed of substances min¬ 
gled, agitated, and shocked against each other ; and in 
this disorder he supposes the earth to have been just 
at the commencement of the Mosaical creation. When 
the orbit of the comet w^as changed, and more regular¬ 
ly wheeled round the sun, every thing took its proper 
place, every part of the surrounding fluid then fell into 
a certain situation, according as it was light or heavy. 
The middle or central part which always remained un¬ 
changed, still continued so; retaining a part of that heat 
which it received in its primeval approaches towards the 
sun; which heat he calculates may continue about six 
thousand years. Next to this, fell the heavier parts of 
the chaotic atmosphere, which served to sustain the 
lighter : but as in descending, they could not entirely 
be separated from many watery parts, with which 


* See Dr, Keill’s examination and remarks on this theory. 



THEORIES OF THE EARTH. 


95 


they were intimately mixed, they drew down these 
also along with them ; and these could not ascend 
again after the surface of the earth was consolidated,. 
Thus, the entire body of the earth was composed, next 
the centre, of a great burning globe of more than 2000 
leagues in diameter: next to this, is placed a heavy 
earthy substance which encompasses it ; round which 
is circumfused a body of water ; and upon this body 
of water is placed the crust which we inhabit. The 
body of the earth being thus formed, the air, which is 
the lightest substance of all, surrounded its surface, 
and the beams of the sun darting through, produced the 
light, which, we are told by Moses, first obeyed the Di¬ 
vine command. 

The whole economy of the creation being thus ad¬ 
justed, it only remains to account for the risings and de¬ 
pressions on its surface, with other seeming irregulari¬ 
ties of its appearance. The hills and valleys are by 
him supposed to be formed by their pressing upon the 
Internal fluid, which sustains the external shell of earth, 
with greater or less weight: those parts of the earth 
which are heaviest, sink the lowest into the fluid, and 
thus become valleys; those that are lightest rise higher 
upon the earth’s surface, and are called mountains. 
Such was the face of nature before the deluge ; the 
earth was then more fertile and populous than at pres¬ 
ent : the lives of men and animals were extended to 
ten times their present duration, and all these advanta¬ 
ges arose from the superior heat of the central globe, 
which has ever since been cooling. 

To account for the deluge, he says, that a comet de¬ 
scending in the plane of the ecliptic towards its perihe¬ 
lion, on the first day of the deluge, passed just before 
the body of the earth. This comet, when it came be¬ 
low the moon, would raise a vast and strong tide, both in 
the seas that were on the surface, and in the abyss which 
was under the upper crust of the earth, in the same 
manner as the moon at present raises the tides in the 
ocean. That these tides would begin to rise and in¬ 
crease during the approach of the comet, and would be 
at their greatest height when the comet was at its least 
distance from the earth. By these tides, caused by the 
attraction of the comet, he supposes that the abyss 


96 


THEORIES OF THE EARTH. 


would assume an elliptical figure, the surface of which, 
being much larger than the former spherical one, the 
exterior crust of earth must conform itself to the same 
figure. But as the external crust was solid and com¬ 
pact, it must of necessity, by the violent force of the 
tide, be stretched and broken."^ This comet, by pass¬ 
ing close by the earth, involved it in its atmosphere and 
tail for a considerable time, and left a prodigious quan¬ 
tity of vapours on the earth’s surface. These vapours 
being yery much rarefied after their primary fall, would 
be immediately drawn up into the air again, and after¬ 
wards, descend in violent rains, and would be the cause 
of the forty days rain mentioned in the Scripture. 

The rest of the water was forced upon the surface of 
the earth by the vast and prodigious pressure of the in¬ 
cumbent water derived from the comet’s atmosphere, 
which sunk the outward crust of the earth in the abyss. 
By these means, he supposes that there was water 
enough brought on the surface, to cover the whole face 
of the earth, to the perpendicular height of three miles. 
And, to remove this body of water, he supposes the 
wind dried up some, and forced the rest through the 
cracks and fissures of the earth into the abyss, whence 
great part of it had issued. 

i. BUFFON’S THEORY. 

M. De Buffon begins his theory by attempting to 
prove that this world, which we inhabit, is nothing more 
than the ruins of a world. “ The surface of this im¬ 
mense globe, (says he) exhibits to our observation, 
heights, depths, plains, seas, marshes, rivers, caverns, 
gulphs, volcanoes ; and on a cursory view, we can dis¬ 
cover in the disposition of these objects, neither order 


* How was the ark preserved during this commotion ? To preserve 
the ark, without the immediate protection of Providence, it would be 
necessary, that the flood of water should be perfectly calm, and free 
from storms and tempests ; but, if the waters were smooth, and under¬ 
went no violent agitattion, how could shells and marine bodies be 
thrown upon the land on the tops of mountains, or be buried many 
feet deep in the earth ? The calm sea, necessary for preserving the 
ark, could move none of the shells ; and the rough sea, necessary for 
transporting the shells, would destroy the ark. 



THEORIES OF THE EARTH. 


97 


aor regularilj. If we penetrate into the bowels of the 
earth, we find metals, minerals, stone, bitumens, sands., 
earths, waters, and matter of every kind, placed, as it 
were, by mere accident, and without any apparent de¬ 
sign. Upon a nearer and more attentive inspection, we 
discover sunk mountains, caverns filled up, shattered 
rocks, whole countries swallowed up, new islands emerg¬ 
ed from the ocean, heavy substances placed above light 
ones, hard bodies enclosed within soft bodies: in a word, 
we find matter in every form, dry and humid, warm and 
cold, solid and brittle, blended in a chaos of confusion, 
which can be compared to nothing but a heap of rub¬ 
bish, or the ruins of a world.’’ In examining the bottom 
of the sea, he observes, that we perceive it to be equal¬ 
ly irregular as the surface of the dry land. We dis¬ 
cover hills and valleys, plains and hollows, rocks and 
earths of every kind ; we discover, likewise, that islands 
are nothing but the summits of vast mountains, whose 
foundations are buried in the ocean. We find other 
mountains whose tops are nearly on a level with the sur¬ 
face of the water ; and rapid currents which run con¬ 
trary to the general movements ; these, like rivers, never 
■exceed their natural limits. The bottom of the ocean 
and shelving sides of rocks produce plentiful crops of 
plants of many different species : its soil is composed of 
«and, gravel, rocks, and shells ; in some places it is fine 
clay, in others, a compact earth : and in general, the 
bottom of the sea has an exact resemblance to the dry 
land which we inhabit. In short, Buffon supposed 
that the dry land was formerly the bottom of the sea : 
he «ays, moreover, that it is impossible that the shells 
and marine substances which we find at an immense 
depth in the earth, and even in rocks and marble, should 
have been the effects of the deluge: for the waters 
could not overturn, and dissolve the whole surface of 
the earth, to the greatest depths. The earth must, 
therefore, have been originally much softer than it now 
is, and that it is has acquired its present solidity by the 
continual action of gravity, and consequently, the earth 
is much less subject to change now than formerly. 

With regard to the original formation of the earth and 
all the planets in our system, he supposes that they were 
detached from the sun all at once by a mighty stroke of 
15 


98 


THEORIES OF THE EARTH. 


a comet not in the form of globes, but in the form of 
torrents; the motion ot the foremost particles being ac¬ 
celerated by those which immediately followed, and the 
attraction ot the foremost particles would accelerate the 
motion of the hindmost; and that the acceleration pro¬ 
duced by one or both of these causes might be such as 
would necessarily change the original motion arising 
from the impulse of the comet; and a motion might re¬ 
sult similar to that which takes place in the planets. 
The revolution of the primary planets on their axes, he 
accounts for from the obliquity of the original stroke, 
impressed by the cometf—“It is therefore evident, 
says he, that the earth assumed its figuie when in a 
melted state; and to pursue our theory, it is natural to 
think that the earth, when it issued from the sun, had 
no other form but that of a torrent of melted and inflamed 
matter; that this torrent, by the mutual attraction of its 
parts, took on a globular figure, which its diurnal motion 
changed into a spheroid : that when the earth cooled, 
the vapours which were expanded like the tail of a 
comet, gradually condensed, and fell down in the form 
of water upon the surface, depositing at the same time a 
slimy substance mixed with sulphur and salts; part of 
which was carried by the motion of the waters into the 
perpendicular fissures of the strata, and produced me¬ 
tals ; and the rest remained on the surface, and gave rise 
to the vegetable mould which abounds in different pla¬ 
ces, the organization of which is not obvious to our sen¬ 
ses. 

Thus the interior parts of the globe were originally 
composed of vitrified matter. Above this vitrified mat¬ 
ter were placed those bodies which the fire had re¬ 
duced to Ihe smallest particles, as sands, which are only 
portions of glass ; and above these pumice-stones and 
the scoriae of melted matter, which produced the differ¬ 
ent clays. The whole was covered with water to the 
depth of 500 or 600 feet which originated from the con¬ 
densation of vapours when the earth began to cool. This 


* Here Mr. BufFon loses hiraself in conjecture, scarcely within the 
verge of possibility, and very improbable. 

t This is a wild theory to , account for the diurnal motion of the 
earth and other planets 5 ’ 



THEORIES OF THE EARTH. 


99 


water deposited a stratum of mud, mixed with all those 
matters which are capable of being sublimed or exhaled 
by fire ; and the air was formed of the most subtile va¬ 
pours, which, from their levity, rose above the water. 

Such was the condition of the earth when the tides, 
the winds, and the heat of the sun began to introduce 
changes on its surface. The diurnal motion of the earth, 
and that of the tides, elevated the waters in t he equato¬ 
rial regions, and necessarily transported thither great 
quantities of slime, clay, and sand ; and by thus elevating 
those parts of the earth, they perhaps sunk those under 
the poles about two leagues, ora 230th part of the whole; 
for the waters would easily reduce into powder, pumice- 
stones, and other spongy parts of the vitrified matter 
upon the surface, and by this means excavate some pla¬ 
ces and elevate others, which, in time, would produce isl¬ 
ands and continents, and all those inequalities on the sur¬ 
face, which are more considerable towards the equator 
than towards the poles.” 

5. Dr. HUTT0N‘S THEORY. 

In the first volume of the Edinburgh Philosophical 
Transactions, Dr. Hutton has laid down a new theory of 
the earth, perhaps the most elaborate and comprehen¬ 
sive that has hitherto appeared ; to give a general ab¬ 
stract of it would much exceed the bounds allotted to 
this chapter. Wherefore, all that can be done here is, to 
point out some of the most striking passages. 

He says, the general view of the terrestrial system 
conveys to our mind a fabric erected in wisdom, and 
that it was originally formed by design as an habitation 
for living creatures. In taking a comprehensive view of 
the mechanism of the globe, we observe three principal 
parts of which it is composed, and which, by being pro ¬ 
perly adapted to one another, form it into an habitable 
world; these are the solid body of the earth, the waters 
of the ocean, and the atmosphere surrounding the whole. 
On these Dr. Hutton observes ; 

1. The parts of the terrestrial globe more immediate¬ 
ly exposed to our view, are supported by a central body, 
commonly supposed, but without any good reason, to be 
solid and inert. 


10« 


THEORIES OF THE EARTH. 


2. The aqueous pari, reduced to a spherical form hy 
gravitation, has become oblate bj the earth’s centrituga^ 
force. Its use is to receive the rivers, be a fountain of 
vapours, and to afford life to innumerable animals, as 
well as to be the source of growth and circulation to the 
organized bodies of the earth. 

3. The irregular body of land raised above the level 
of the sea, is by far the most interesting, as immediately 
necessary to the support of animal life. 

4. The atmosphere surrounding the whole is evident¬ 
ly necessary for Innumerable purposes of life and vege¬ 
tation, neither of which could subsist a moment without 
it. 

Having thus considered the mechanism of the globe, 
he proceeds to investigate the powers by which it is up¬ 
held : these are the gravitating and projectile forces by 
which the planets are guided ; the influence of light and 
heat, cold and condensation: to which may be added 
electricity and magnetism. 

With regard to the beginning of the world, though 
Dr. Hutton does not pretend today aside the Mosaic ac¬ 
counts respecting the origin of man, yet he endeavours 
to prove, that the marine* animals are of much higher 
antiquity than the human race. 

The solid parts of the globe are, in general, composed 
of sand, gravel, argiflaceous and calcareous strata, or of 
these mixed with some other substances. 

Sand is separated and sized by streams and currents ; 
gravel is formed by the mutual attrition of stones agita¬ 
ted in water; and marly or argillaceous strata have been 
collected by subsiding in water in which those earthy 
substances had floated. Thus, so far as the earth is 
formed of these materials, it would appear to have been 
the production of water, wind, and tides. 

The doctor’s next inquiry, is into the origin of our 
knd, which he seems willing to derive entirely from the 
exuviae of marine animals.f After adducing some argu- 


* According to the Mosaic account of tlie creation, the marine ani¬ 
mals were created the fifth day, and man: the sixth. 

t To give this any appearance of probability, the marine animals 
must have been created many centuries before either the dry land or 
the land animals were created ; yet, according to the-Mosaic account oP 
creation, the dry land appeared on the third day ! 



THEORIES OE THE EARTH. 


101 


jnents in support of this opinion, the principal of which 
is drawn from the quantity of marine productions found 
in f^ifferent parts of the earth, he says, “ The general 
amount of our reasoning is this; that nine-tenths per¬ 
haps, or 99 hundredths of this earth, so far as we see, 
have been formed by natural operations of the globe, in 
collecting loose materials, and depositing them at the 
bottom of the sea, consolidating those collections in va¬ 
rious degrees, and either elevating these consolidated 
masses above the level on which they were formed, or 
lowering the level of that sea.” 

With respect to the different strata, he thinks it most 
probable that they have been consolidated by heat and 
fusion ; and this hypothesis he imagines, will solve every 
difficulty respecting them; and, as ihe question is of the 
greatest importance in natural history, he discusses it to 
a considerable length. He considers metals of every 
species as the vapour of the mineral regions, condensed 
occasionally in the crevices of the land. 

His next consideration is the means by which the dif¬ 
ferent strata have been elevated from the bottom of the 
ocean ; (for he looks upon it as an indubitable fact that 
the highest points of our land have been for ages at the 
bottom of the ocean ;) and concludes, that the land on 
which we dwell has been elevated from a lower sifuation 
by the same agent which has been employed in consoli¬ 
dating the strata, in giving them stability, and preparing 
them for the purpose of the living \Torld. This agent is 
matter, actuated by extreme heat, and expanded with 
amazing force. 

The doctor imagines the world to be eternal, and en¬ 
dued with renovating power ; for he says, “ When the 
former land of this globe had been complete, so as to 
begin to waste and be impaired by the encroachment of 
the sea, the present land began to appear above the sur¬ 
face of the ocean. In this manner, we suppose a due pro¬ 
portion of land and water to be always preserved upon the 
surface of the globe, for the purpose of a habitable world, 
such as we possess.” After endeavouring to prove a 
succession of worlds in the system of nature, he con¬ 
cludes his dissertation in these words ; “ The result, 
therefore, of our present inquiry is, that we find no ves¬ 
tige of a beginning, no prospect of an end.” 


102 


THEORIES OF THE EARTH. 


6. Mr. WHITEHURST’S THEORY. 

Mr. Whitehurst first proceeds to show, that all fluid 
bodies, which do not revolve about their axis, assume 
spherical forms, from the mutual attraction of their com¬ 
ponent parts ; and thence infers, that all bodies, naturally 
spherical, have been originally in a state of fluidity. 
Again, as it is a known principle in the laws of motion, 
that, if any fluid body turn on its axis, it will, by ihe 
centrifugal force, depart from a spherical form, and as¬ 
sume that of an oblate spheroid ; and, as the earth is 
known to be such a figure, agreeing with the laws of 
gravity, fluidity, and centrifugal force, he suppdses that 
the earth was originally a fluid, composed of chaotic, 
heterogeneous matter, which acquired its present form 
by revolving on its axis in that state of fluidity ; and that 
its diurnal and annual rotations have suffered no change, 
but have performed equal rotations in equal times, from 
the moment of its first existence to the present era. 

This heterogeneous mass, being totally unfit for ani¬ 
mal or vegetable life, was not instantaneously but pro¬ 
gressively formed into an habitable world. As soon as 
the component parts of the chaos became quiescent, 
similar particles began to unite and compose bodiesof 
various denominations, viz. the particles of air united 
with those of air, those of water with water, and those 
of earth with earth. Bodies of the greatest density 
began their approach towards the centre of gravity, and 
those of the greatest levity ascended towards the sur¬ 
face. Thus, apparently, commenced the separation of 
the chaos into air, water, earth, and other select bodies. 
As the earth consolidated more and more towards its 
centre, its surface became gradually covered with wa¬ 
ter, until the sea prevailed universally over the whole 
earth. At this time the marine animals were created, 
and multiplied so exceedingly, as to replenish the ocean 
from pole to pole. 

The sun and moon were coeval with the creation of 
the earth, and, as the atmosphere was progressively 
freed from heterogeneous substances, light and heat 
gradually increased until the sun became visible in the 
firmament, and shone with its full lustre and brightness. 


THEORIES OF THE EARTH. 


103 


The attractive influence of the sun and moon, inter¬ 
fering with the regular and uniform subsiding of the sol¬ 
ids of the earth, caused the sea to be unequally deep, 
and, consequently, the dry land to appear. Hence, the 
primitive islands were gradually formed by the flux and 
reflux of the tides, and in process of time, became firm 
and drj^ fit for the reception of the vegetable and ani¬ 
mal kingdoms. The ocean being plentifully stocked 
With inhabitants, previous to the appearance of dry land, 
many of these animals became daily enveloped and 
buried in the mud, in all parts of the sea from pole to 
pole, by the daily action of the tides. 

As the central parts of the earth began to consolidate 
before the superficial parts thereof, the former became 
ignited before the latter. As the subterraneous fire 
gradually increased, its expansive force likewise increas¬ 
ed till it became superior to the incumbent weight, and 
distended the strata like a bladder forcibly blown ; and 
as the subterraneous fire operated universally in the 
same stratum, and with the same degree of force, it ap¬ 
pears most probable that the deluge, or Noah’s flood, 
prevailed universally over the whole earth. 

The expansive force of subterraneous fire still increas¬ 
ing, it became superior to the incumbent weight and co¬ 
hesion, of the strata, which were then burst, and opened 
a communication between the two oceans of melted mat¬ 
ter and water ; by these two different elements corning 
in contact, the latter became instantly converted into 
steam, and produced an explosion infinitely beyond all 
human conception. The terraqueous globe being thus 
burst into millions of fragments,* the strata were broken, 
and thrown into every possible degree of confusion and 
disorder ; hence, those mighty eminences, the Alps, the 
Andes, the Pyrenean, and all other chains of mountains, 
were brought from beneath the deep ; for the earth, in 
its primitive state, was perfectly level. 

Hence, the sea retired from those vast tracts of land, 
the continents, into the caverns, became fathomless, and 


* We are in the same dilemma here with respect to the preservation 
of Noah and the Ark, as in Burnetts and Whiston’s theories ; besides, 
the noise of such an explosion as above described, would forever den 
prive any human being of the noble faculty of hearing. 



104 


THE ATMOSPHERE, kc. 


environed with craggy rocks, cliffs, and impeiidiiii; 
shores, and its bottom spread over with mountains and 
valleys, like the land. 

As mountains and continents were not primary pro¬ 
ductions of nature, but produced at the time of the del¬ 
uge, the inclemencies of the seasons were totally un¬ 
known in the antediluvian state of nature ; an uniform 
temperature universally prevailed in the atmosphere ; it 
was not subject to storms and tempests, and consequent¬ 
ly, not to rain ; and as there was no rain, most certain¬ 
ly there was no rainbow. 

On account of the small elevations of the primitive 
islands, and the inferiority of their superficies to that of 
continents, the surface of the sea, and the quantity of 
aqueous particles exhaled, were proportionably greater. 
The atmosphere was thus plentifully saturated with hu¬ 
midity, which descended copiously in dews, during the 
absence of the sun, and abundantly replenished the 
earth. 


CHAP. IX. 

Of the Atmosphere, Air, JVinds, and Hurricanes* 

THE earth is surrounded by a thin fluid mass of mat¬ 
ter, called the atmosphere : this matter gravitates to¬ 
wards the earth, revolves with it in its diurnal motion, 
and goes round the sun with it every year. Were it 
not forthe atmosphere, which abounds with particles ca¬ 
pable of reflecting light in all directions, only that part 
of the heavens would appear bright in which the sun 
was placed,* and the stars and planets would be visible 
at mid-day ;f but, by means of an atmosphere, we enjoy 
the sun’s light (reflected from the aerial particles con- 


* Dr. Keill, Lect. xx. 

t M de Saussure, when on the top of Mont Blanc, which is eleva¬ 
ted 5101 yards above the level of the sea, and where, consequently, the 
atmosphere must be more rare than ours, says, that the moon shone 
with the brightest splendour in the midst of a sky as black as ebony; 
while Jupiter, rayed like the sun, rose from behind the mountains in the 
east. Append, vol. 74, Monthly Review. 



THE ATMOSPHERE, ice. 


105 


lainedin the atmosphere) for sometime before he rises, 
and after he sets ; for, on the 21st of June at London, 
the apparent day is 9m. KJsec. longer than the astro¬ 
nomical day.* This invisible fluid extends to an un¬ 
known height; but if, as astronomers generally estimate, 
the sun begins to enlighten the atmosphere in the morn¬ 
ing when he comes within 18 degrees of the horizon of 
any place, and ceases to enlighten it when he is again 
depressed more than 18 degrees below the horizon in 
the evening, the height of the atmosphere may easily be 
calculated to be nearly 50 miles.f Notwithstanding 
this great height of the atmosphere, it is seldom sufficient¬ 
ly dense at two miles high to bear up the clouds ; it be¬ 
comes more thin and rare the higher we ascend. Thit; 
fluid body is extremely light, being at a mean density, 
816 times lighter than water ;J it is likewise very elas¬ 
tic, as the least motion excited in it is propagated to a 
great distance : it is invisible, for we are only sensible 
of its existence from the effects it produces. It is capa¬ 
ble of being compressed into a much less space than 
what it naturally possesses, though it cannot be congeal¬ 
ed or fixed as other fluids may ; for no degree of cold 
has ever been able to destroy its fluidity. It is of differ¬ 
ent density in every part upwards from the earth’s sur¬ 
face decreaEflng in its weight the higher it rises ; and 
consequently, must also decrease in density. The 
weight or pressure of the atmosphere upon any portion 
of the earth’s surface is equal to the w eight of a column 


* See Keith^s Trigonometry, second edition, page 266. 
t Let ArB (Plate III. Figure 5.) represent the horizon of an ob- 
sen^eratA; Sr a ray of light falling upon the atmosphere at r, and- 
making an angle SrB of 18 degrees with the horizon (the suu being sup¬ 
posed to have that depression) the angle Sr A will then be 162 degrees. 
From the centre O of the earth draw Or, and it will be pei pendicular 
to the reflecting particles at r ; and, by the principles of optics, it will 
likewise bisect the angle Sr A. In the right angled triangle OAr, the 
angle Or A=81®, AO=S982 miles, the radius of the earth. Hence, hy 
trigonometry. 

Sine of Or A, 81® - - 9.9946199 

Is to AO, S982 - - - S.600101S 

As radius, sine of 90* * - 10.0000000 

Is to Or 4031.76 • - - 3.6054814 

Now, if from Or=4031.6, there be taken 0V=0 1=3982, the 
jnainder Vr=49,6 miles is the height of the atmosphere. 

$ Dr. Thom8on’'8 Chemistry, vol. iv. page 7, edition of 1810<, 

J6 



106 


THE ATxMOSPHERE, &c. 


of mercury which will cover the same surface, and 
whose height is from 28 to 31 inches : this is proved by 
experiment on the barometer, which seldom exceeds the 
limits above-mentioned. Now, if we estimate the di¬ 
ameter of the earth at 7964* miles, the mean height of 
the barometer at 29i inches, and a cubic foot of mercu¬ 
ry to weigh 13500 ounces avoirdupois, the whole weight 
of the atmosphere will be 11522211494201773089 lbs. 
avoirdupois, and its pressure upon a square inch of the 
earth’s surface 14| lbs. 

The atmosphere is the common receptacle of all the 
effluvia or vapours arising from different bodies, viz. of 
the steam or smoke of things melted or burnt; of the 
fogs or vapours proceeding from damp, watery places ; 
of steams arising from the perspiration of whatever en¬ 
joys animal or vegetable life, and of their putrescence 
when deprived of it; also, of the effluvia proceeding 
from sulphureous, nitrous, acid, and alkaline bodies, &c. 
which ascend to greater or less heights according to 
their specific gravity. Hence, the difficulty of deter¬ 
mining the true composition of the atmosphere. Chem¬ 
ical writers,! however, have endeavoured to show, that 
it consists chiefly of three distinct elastic fluids, united 
together by chemical affinity; namely air, vapour or 
water, and carbonic acid gas, J differing in their propor- 


* The diameter of the earth in inches will be 504599040 ; and the 
diameter with the atmosphere 504599099 inches, the difference be¬ 
tween the cubes of these diameters multiplied by .5236, gives 
23597489140125231287.S564 cubic inches in the atmosphere. Now, 
if 1728 cubic inches weigh 1S500 ounces, as stated by Dr. Thomson, 
page 6, vol. iv. of bis chemistry, the weight of the atmosphere will be 
determined as above. If the square of the diameter 504599040 be mul¬ 
tiplied by 3.1416, the product will give the superficies of the earth, 
=799914792576234098.56 square inches ; and if the weight of the at¬ 
mosphere be divided by this superficies, the quotient will be 14.4 lbs. 
=14f lbs. the pressure of the atmosphere on every square inch of the 
earth’s surface. The pressure of the atmosphere on a square inch of sur¬ 
face, may likewise be found by experiments made with the air-pump, or 
by weighing a column of mercury whose base is one inch square, and 
height 29^ inches. 

t Dr. Thompson’s Chemistry, page 34, vol. iv. edition of 1810. 

I Gas is a terra applied by Chemists to all permanently elastic 
fluids, except common air ; and carbonic acid gas is what was former¬ 
ly called fixed air, or such as extinguishes flame, and destroys animal 
life. 



THE ATMOSPHERE, &c. 


107 


lions at different times and in different places ; but the 
average proportion of each, supposing the whole atmos¬ 
phere to be divided into 100 ecpial parts, is given by 
Dr. Thompson as follows : 

air, 

1 vapour, or water, 
carbonic acid, 

100 


Hence, it appears, that the foreign bodies which are 
mixed or united with the air in the atmosphere, are so 
minute in quantity, when compared with it, that they 
have no very sensible influence on its general properties ; 
wherefore, in describing the mechanical properties of 
the air, in the succeeding parts of this chapter, no atten¬ 
tion is paid to its component parts in a chemical point 
of view ; but wherever the word air occurs, common or 
atmospheric air is always meant. It may, however, be 
proper to remark here, that from various experiments,* 
chemists have inferred, that if atmospheric air be divi¬ 
ded into 100 parts, 21 of those parts will be vital air, and 
79 poisonous ; hence, the vital air does not compose one 
third of the atmosphere. 

Air is not only the support of animal and vegetable 
life, but is the vehicle of sound ; and this arises from 
its elasticity ; for a body being struck, vibrates, and 
communicates a tremulous motion to the air; this mo¬ 
tion acts upon the cartilaginous portion of the ear, where 
there are several well contrived eminences and concavi¬ 
ties to convey it into the auditory passage, where it 
strikes on the membrana tympani, or drum of the ear, 
and produces the sense of hearing. 


* Dr. Thompson, vol.iv. page 20, of his Chemistry, says, “ Whatever 
method is employed to abstract oxygen from air, the result is uniform. 
They all indicate, that common air consists very nearly of 12 parts of 
pxygen and 79 of azote.” 

21 oxygen gas (viz. vital air.) 

79 azotic gas (viz. poisonous air.) 


100 




108 


THE ATMOSPHERE, &c. 


From (he fluid state of the atmosphere, its great sub» 
(ilty and elasticity, it is susceptible of the smallest mo¬ 
tion that can be excited in it; hence, it is subject to the 
disturbing forces of the moon and the sun; and tides 
will be generated in the atmosphere similar to the tides 
in the ocean. By the continual motion of the air, nox¬ 
ious vapours, which are destructive to health, are in 
some measure dispersed ; so (hat the air, like the sea, is 
kept from putrefaction by winds and tides. 

Air may be vitiated, by remaining closely pent up in 
any place for a considerable length of time ; and, when 
it has lost its vivifying spirit, it is called damp or fixed 
air, not only because it is filled with humid or moist va¬ 
pours, but because it deadens fire, extinguishes flame, 
and destroys life. 

If part ot the vivifying spirit of air, in any country, 
begin to putrefy, the inhabitants of that country, will be 
subject to an epidemical disease, which will continue 
until the putrefaction is over ; and as the putrefying 
spirit occasions this disease, so, if the diseased body 
contribute towards the putrefying of the air, then the dis¬ 
ease will not only be epidemical, but pestilential and con¬ 
tagious. 

The air will press upon the surfaces of all fluids, with 
any force, without passing through them or entering into 
them ; so that the softest bodies sustain this pressure 
without suffering any change in their figure, and the 
most brittle bodies bear it without being broken. Thus 
the weight of the atmosphere presses upon the surface 
of water, and forces it up into the barrel of a pump. It 
likewise keeps mercury suspended at such a height, that 
its weight is equal to the pressure, and yet, it never 
forces itself through the mercury into the vacuum a-» 
bove. 

Another property of the air is, that it is expanded by 
heat, and condensed or contracted by cold : hence, the 
fire rarefying and attenuating the air in the chimnies, 
causes it to ascend the funnels, while the air in the 
room, by (he pressure of the atmosphere, is forced to 
supply the vacancy, and rushes into the chimney in a 
constant torrent, bearing the smoke into the higher re¬ 
gions of the atmosphere. In large cities, in the winter, 
when there are many fires, people and animals, the air is 


THE ATMOSPHERE, &c. 


109 


considerably more rarefied than in the adjoining coun¬ 
try ; for which reason, continual currents of colder air 
rush in at all the exterior streets, bearing up the rarefied 
and contaminated air above the tops of the houses and 
the highest buildings, and supplying its place with air 
of a more salubrious cpiality. The more extensive winds 
owe their origin to the heat of the sun; this heat acting 
upon some part of the air causes it to expand, and be¬ 
come lighter, and, consequently, it must ascend; while 
the air adjoining, which is more dense and heavy, will 
press forward towards the place where it is rarefied. 
Upon this principle, we can easily account for the trade 
winds, which blow constantly from east to west about 
the equator ; for when the sun shines perpendicularly on 
any part of the earth, it will heat and rarefy the air in 
that part, and cause it to ascend ; while the adjacent air 
will rush in to supply fits place, and consequently, will 
cause a stream or current of air to flow from all parts to¬ 
wards that which is the most heated by the sun. But 
as the sun, with respect to the earth, moves from east to 
west, the common course of the air will be from east to 
west; and, therefore, at or near the equator, where the 
mean heat of the earth is the greatest, the wind will blow 
continually from the east; but on the north side of the 
equator it will decline a little to the north ; and, on the 
south side of the equator it will decline to the south. If 
the earth were covered with water, the motion of the 
wind would follow the apparent motion of the sun, in the 
same manner as the motion of the water would follow the 
motion of the moon ; but, as the regular course of the 
tides is changed by the obstruction of continents, islands, 
&c. so the regular course of the winds is changed 
by high mountains, by the declination of the sun to¬ 
wards the north and south, by burning sands, which re^ 
tain the solar heat to an incredible degree, by the falling 
of great quantities of rain, which causes a sudden con¬ 
densation or contraction of the air, by exhalations that 
rise out of the earth at certain times and places, and 
from various other causes. Thus, according to Dr. Hal¬ 
ley, between the 3d and lOth degree of south latitude, 
the south-east trade-wind continues from April to Octo¬ 
ber ; during the rest of the year, the wind blows from 
the north-west; but between Sumatra and New-Holland 


110 


THE ATMOSPHERE, 


(bis monsoon^ blows from the south during our summer 
months ; it changes about the end of September, and 
continues in the opposite direction till April* 

Over the whole of the Indian Ocean, to the north¬ 
ward of the third degree of south latitude, the north¬ 
east trade-wind blows from October to April, and a 
south-west wind from April to October.f From Borneo, 
along the coast of Malacca, and as far as China, *his 
monsoon, in our summer, blows nearly from the south, 
and in (be winter from the north by east. Near the coast 
of Africa, between Mozambique and Cape Guardafui, the 
winds are irregular during the whole year, owing to the 
different monsoons which surround that particular place. 
Monsoons are likewise regular in the Red Sea ; between 
April and October they blow from the north-west, and 
during the other months from the south-east, keeping 
constantly parallel to the Arabian coast. J 

On (he coast of Brazil, between Cape St. Augustine 
and the island of St. Catherine, from September to 
April, the wind blows from the east or north-east; and 
from April to September it blows from the south-west; 
so that monsoons are not altogether confined to the In¬ 
dian Ocean. 

On the coast of Africa, from Cape Bajador, opposite 
to the Canary Islands, to Cape Verd, the winds are 
generally north-west; and from hence to the island of St. 
Thomas, near (he equator, they blow almost per¬ 
pendicular to the shore. 

In all maritime countries of any considerable extent, 
between the tropics, the wind blows during a certain 
number of hours from the sea, and during a certain num¬ 
ber from the land; these winds are called sea and 
land breezes. During the day, the air above the land is 
hotter and more rare than that above the sea ; the sea 


* The regular winds in the Indian seas are called monsoons, from the 
Malay word tnoossiti, which signifies “ a season.” Forest’s Voyage, 
page 59. 

t The student will find these winds represented on Adams’ globes by 
arrows having the barbed points flying in the direction of the wind as 
if shot from a bow; and, where the winds are variable, these arrows 
seem to be flying in all directions. 

Bruce’s Travels, vol. i. chap. 4. 



THE ATMOSPHERE, &c. 


Ill 


air, therefore, flows in upon the land and supplies the 
place of the rarefied air, which is made to float higher in 
the atmosphere ; as the sun descends, the rarefaction of 
the land air is diminished, and an equilibrium is restor¬ 
ed. As the night approaches, the denser air of the hills 
and mountains (for where there are no hills, there are no 
sea and land breezes,) falls down upon the plains, and 
pressing upon the air of the sea, which has now become 
comparatively lighter than the land air, causes the land 
breeze. 

The Cape of Good Hope is famous for its tempests, 
and the singular cloud which produces them : this cloud 
appears at first only like a small round spot in the 
sky, called by sailors the Ox’s Eye, and which prob¬ 
ably appears so minute from its exceedingly great 
height. 

In Natolia, a small cloud is often seen, resembling 
that at the Cape of Good Hope, and from this cloud a 
terrible wind=^ issues, which produces similar effects. In 
the sea between Africa and America, especially at the 
equator and in the neighbouring parts, tempests of this 
kind very often arise, and are generally announced by 
small black clouds. The first blast which proceeds from 
these clouds is furious, and would sink ships in the open 
sea, if the sailors did not take the precaution to furl their 
sails. The tempests seem to rise from a sudden rare¬ 
faction of the air, which produces a kind of vacuum, and 
the cold dense air rushing to supply the place. 

Hurricanes, which arise from similar causes, have a 
whirling motion which nothing can resist. A calm gen¬ 
erally precedes these horrible tempests, and the sea then 
appears like a piece of glass; but in an instant, the fury 
of the winds raises the waves to an enormous height. 
When, from a sudden rarefaction, or any other cause, 
contrary currents of air meet in the same point, a whirl¬ 
wind is produced. 

The force of the wind upon a square foot of surface is 
nearly as the square of the velocity; that is, if on a 
square board of one foot in surface, exposed to a wind, 


* This wind seems to be described by St. Paul in the 27tb chapter of 
ther Acts, by the name of Euroclydon. 



112 


THE ATMOSPHERE, &c. 


there be a pressure of one pound, another wind, with 
double the velocity, will press the board with a force of 
four pounds, &c. The following table, extracted from 
the Philosophical Transactions, shows the velocity and 
pressure of the winds according to their different appel¬ 
lations. 


Velocity of the Wind. 


Perpendicular 
force on one 


Common appellations of 


Miles in one 
hour. 


Feet in one 
second. 


square foot, in 
pounds avoir¬ 
dupois. 


the winds. 


1 


2 

3 

i 

5 

10 

15 

20 

25 

SO 

35 

40 

45 

50 


60 

80 


1.47 
2.93 I 
4.40^ 
5.87 I 
7.33 ( 

14.67 I 

22.00 S 

29.34 i 

36.67 i 
44.01 I 

51.34 I 

58.68 I 

66.01 I 

73.35 

88.02 

117.36 


.005 
. 020 ? 
.044 ( 
.079 I 
•123 I 
.492 I 
1.107 I 
1.968 I 
3.075 i 
4.429 I 
6.027 S 
7.873 ■> 
9.9635 
12.300 
17.715 
31.490 


Hardly perceptible. 
Just perceptible. 

Gentle pleasant wind. 
Pleasant brisk gale. 
Very brisk. 

High winds. 

Very high. 

A storm or tempest. 

A great storm. 

A hurricane. 


100 


146.70 


49.200 


A hurricane that tears 
up trees, and carries 
buildings, Sec. before it. 











rAPOURS, FOGS, CLOUDS, &t. 


113 


CHAPTER X. 

Of FdpotirSf Fogs and Mists, Clouds, Dew and Hoar- 
Frost, Fain, Snow and Hail, Thunder and Light¬ 
ning, Falling Stars, Ignis Fatuus^ Aurora Borea¬ 
lis, and the Rainbow, 

1. VAPOURS are composed of aqueous or watery 
particles, separated from the surface of the water, or 
moist earth, by the action of the sun’s heat; whereby 
Uiey are so rarefied, attenuated, and separated from 
each other, as to become specifically lighter than the 
air; and, consequently, they rise and float in the atmos¬ 
phere. 

2. Fogs and mists. Fogs are a collection of vapours 
which chiefly rise from fenny, moist places, and become 
more visible as the light of the day decreases. If these 
vapours be not dispersed, but unite with those that rise 
from water, as from rivers, lakes, &c. so as to fill the air 
in general, they are called mists. 

3. Clouds are. generally supposed to consist of va¬ 
pours exhaled from the sea and land.* These vapours 
ascend till they are of the same specific gravity as the 
surrounding air: here they coalesce, and by their union 
become more dense and weighty. The more thin and 
rare the clouds are, the higher they soar, but the height 


* Dr. Thompson, in vol.iv. of his Chemistry, page 79, &c. edition of 
1810, says, it is remarkable that, though the greatest quantity of va¬ 
pours exists in the lower strata of the atmosphere, clouds never begin 
to form there, but always at some considerable height. The heat of the 
clouds is sometimes greater than that of the surrounding air. The for¬ 
mation of clouds and rain is neither owing to the saturation of the at¬ 
mosphere, nor the diminution of heat, nor the mixture of airs of differ¬ 
ent temperatures. Evaporation often goes on for a month together in 
hot weather, especially in the torrid zone, without any rain. The wa¬ 
ter can neither remain in the atmosphere, nor passthrough it, in a state 
of vapour: What then becomes of the vapour after it enters the atmos¬ 
phere ? What makes it lay aside the new form which it must have assu¬ 
med, and return again to its state of vapour, and fall down in rain ? 
Till these questions are experimentally answered, Dr. Thompson con¬ 
cludes, that the formation of clouds and rain cannot be accurately ac¬ 
counted for. 


17 



114 


VAPOURS, FOGS, CLOUDS, &c. 


seldom, if ever, exceeds two miles. The generality of 
clouds are suspended at the height of about a mile ; 
sometimes, when (he clouds are highly electrified, their 
height is not above seven or eight hundred yards. The 
wonderful variety in the colour of the clouds is owing to 
their particular situation to the sun, and the different re¬ 
flections of his light. The various figure of the clouds 
probably proceeds from their loose and voluble texture, 
revolving in any form according to the different force of 
the winds, or from the electricity contained in them. 

The general colour of the sky is blue, and this is oc¬ 
casioned by the vapours which are always mixed with 
air, and which have the property of reflecting the blue 
rays more copiously than any other.* 

4. Dew. When the earth has been heated in the day¬ 
time by the sun, it will retain that heat for some time af¬ 
ter the sun has set. The air being a less dense, or less 
compact substance, will retain the heat for a less time : 
so that in the evening, the surface of the earth will be 
warmer than the air about it, and consequently, the va¬ 
pours will continue to rise from the earth ; but, as these 
vapours come immediately into a cool air, they will only 
rise to a small height; as the rarefied air in which they 
began to rise becomes condensed, the small particles of 
vapours will be brought nearer together. When many 
of these particles are united, they form dew; and, if this 
dew freeze, it will produce hoar-frost. 

5. Rain. When the weight of the air is diminished, 
its density will likewise be diminished, and consequent* 
ly, the vapours that float in it will be less resisted, and 
begin to fall, and, as they begin to strike one upon ano¬ 
ther in falling, (hey will unite and form small drops. But 
when the small drops of which a cloud consisted are uni¬ 
ted into such large drops, that no part of the atmosphere 
is sufficiently dense to produce a resistance able to sup¬ 
port them, they will then fall to the earth, and consti¬ 
tute what we call rain. If these drops be formed in the 
higher regions of the atmosphere, many of them will be 
united before they come to the ground, and the drops 


* Saussure, Voyages dansles Alpes, vol. iv.p 2C8, 




VAPOURS, FOGS, CLOUDS, &c. 


115 


of rain will be very large.♦ The drops of rain increase 
so much both in bulk and motion, during their descent, 
that a bowl placed on the ground would receive in a 
shower of rain, almost twice the quantity of water that a 
similar^bowi would receive on a neighbouring high stee¬ 
ple.f The mean annual quantity of rain is greatest 
at the equator, and decreases gradually as we approach 
the poles. Thus, at 

Latitude. Depth of rain. 

J Grenada, West-Indies, - 1 * 2 ° 0 ' 126 inches. 

St Domingo, Cape St. Fran 9 ois, 19** 46' 120 

Calcutta, - - - - 22 ° 23' - 81 

In England, . . - 53 ® 0 ' - 32 

Petersburg, - - - - 59° 16' - 16 

On the contrary, the number of rainy days is smallest 
at the equator, and increases in proportion to ^4he dis¬ 
tance from it. The number of rainy days is often great¬ 
er in winter than in summer ; but the quantity of rain is 
greater in summer than in winter. More rain falls in 
mountainous countries than in plains. Among the Andes, 
it is said to rain almost perpetually, while in the plains 
of Peru and in Egypt, it hardly ever rains at all. The 
mean annual quantity of rain for the whole globe is esti¬ 
mated by Dr. Thompson at 34 inches in depth, hence, 
may be found the whole quantity of rain that falls in a 
year upon the whole surface of the earth and sea, in the 
same manner as the number of cubic inches were found 
in the atmosphere, in chapter IX. of this work. The 
same author observes, that, for every square inch of the 
earth’s surface, about 41 cubic inches of water are annu¬ 
ally evaporated : so that the average quantity of rain is 
considerably less than the average quantity of water 
evaporated. 

Snow and hail. Snow consists of such vapours as 
are frozen while the particles are small; for, if these 


* Dr. Rutherford’s Natural Philosophy, vol. ii. chap. 10. Signior 
Beccaria, whose observations on the general state of electricity in the 
atmosphere have been very accurate and extensive, ascribes the cause 
of hail, rain, snow, &c. &c. to the effect of a moderate electricity in the 
atmosphere. 

t Mr. Adam Walker’s Familiar Philosophy, lect. v. page 215. 
j Dr. Thompson’s Chemistry, vpl, iv. p. 83, &c. edition of 1810, 



116 


TAPOUR?, FOGS, CLOUDS, &c. 


stick fogellier, after they are frozen, the mass that is form¬ 
ed out of them will be of a loose texture, and form little 
flakes or fleeces, of a white substance, somewhat heavier 
than the air, and therefore, will descend in a slow and 
gentle manner through it. Hail, which is a more com¬ 
pact mass of frozen water, consists of such vapours as 
are united into drops, and are frozen while they are 
falling.* 

r. Thunder and lightning. It has been already 
observed, that the atmosphere is the common receptacle 
of all the effluvia, or vapours, rising from different bodies. 
Now, when the effluvia of sulphureous and nitrous bo- 
diesf meet each othec in the air, there will be a strong 
conflict, or fermentation, between them, which will some¬ 
times be so great as to produce fire.J Then, if the ef¬ 
fluvia be combustible, the fire will run from one part to 
another, just as the inflammable matter happens to lie. 
If the inflammable matter be thin and light, it will rise to 
the upper part of the atmosphere, where it will flash 
without doing any harm ; but if it be dense, it will lie near 
the surface of the earth, where, taking fire, it will ex¬ 
plode with a surprising force, and by its beat rarefy and 
drive away the air, kill men and cattle, split trees, walls, 
rocks, &c. and be accompanied with terrible claps of 
thunder. The effects of thunder and lightning are owing 
to the sudden and violent agitation the air is put into, 
together with the force of the explosion. Stones and 
bricks struck by lightning are often found in a vitrified 
state. Signior Beccaria supposes that some stones in 
the earth, having been struck in this manner, gave rise to 
the vulgar opinion of the thunder-bolt. It is now gene¬ 
rally admitted that lightning and the electrical fluid are 
the same.§ 


♦ Rutherford’s Philosophy, vol. ii. chap. 10. 

t Gunpowder, the effects of which are similar to thunder and lij^ht- 
ning, is composed of six parts of nitre, one part of sulphur, and one 
part of charcoal. 

if Professor Winkler’s Philosophy. 

i Signior Beccaria, of Turin, observes, that the atmosphere abounds 
with electricity; and if a cloud which is positively charged (vi^. which 
has more than its natural shape of electrical fluid) pass near another 
cloud which is negatively charged (viz. which has less than its natural 
^|iare of electrical fluid) they will attract each other, and a quick depri- 



VAPOURS, FOGS, CLOUDS, &c. 


117 


8. The falling stars, and other fiery meteors, 
which are frequently seen ata considerable height in the 
atmosphere, and which have received different names 
according to the variety of their figures and size, arise 
from the fermentation of the effluvia of acid and alkaline 
bodies, which float in the atmosphere. When the more 
subtile parts of the effluvia are burnt away, the viscous 
and earthy parts become too heavy for the air to sup¬ 
port, and by their gravity fall to the earth. 

The disappearance of fiery meteors is frequently ac¬ 
companied by a loud explosion like a clap of thunder, 
and heavy stony bodies have been observed to fall from 
them to the earth. Dr. Thompson^ has given a table of 
36 showers of stones, with the places where they fell, 
the dates, and the testimonies annexed. 

These stony bodies, when found, are always hot, and 
their size differs from a few ounces to several tons. 
They are usually round, and always covered with a 
black crust. When broken, they appear of an ash-grey 
colour, and of a granular texture like coarse sand-stone. 
These substances are probably concretions actually 
formed in the atmosphere, but in what manner no ration¬ 
al account has yet been given. 

9. Of the ignis fatuus, commonly called WilU 
wilh-a-Wisp , or Jack-wiih'a-Lantern. This meteor, 
I ike most others, has not failed to attract the attention of 
Philosophical inquirers. Sir Isaac Newton, in his Op¬ 
tical Queries, calls it a vapour shining without heat. 
Various accounts of it may be seen in the Philosophical 
Transactions.! The most probable opinion is, that it 
consists of inflammable air,Jor oleaginous matter, emitted 


vation of the elec.trical fluid will take place; the flash is called lightning, 
the report thunder (the ensuing rollings are only echoes from distant 
clouds;) the water, thus deprived of its usual support, falls down in im¬ 
petuous torrents. 

* Chemistry, edition of 1810, vol. iv. p. 122. 

t Mr. Ray and some others suppose it to be a collection of glow¬ 
worms flying together; but Dr. Derham confuted this opinion. No. 
•411 

^ Inflammable air may be made thus: exhaust a receiver of the air- 
pump, let the air run into it through the flame of the oil of turpentine, 
then remove the cover of the receiver, and hold a lighted candle to the 
air, it will take fire, and burn quicker or slower according to the 
density of the oleaginous vapour. 



ua 


VAl»OUUS, FOGS, CLOUDS, kc. 


from a pulrefaction and decomposition of vegetable sub- 
stances, in marshy grounds; which, being kindled by 
some electric spark, or other cause unknown to us, will 
continue to burn or reflect a kind of thin flame in the 
dark, without any sensible degree of heat, till the mat¬ 
ter which composes (he vapour is consumed. This 
meteor never appears on elevated grounds, because 
they do not sufficiently abound with moisture to produce 
the inflammable air, which is supposed to issue from bogs 
and marshy places. It is often observed flying by the 
sides of hedges, or following the course of rivers; the 
reason of which is obvious, for the current of air is great¬ 
er in these places than elsewhere. These meteors are 
very common in Italy and in Spain. Dr Shaw* has 
described a remarkable ignis fatuus, which he saw in 
the Holy Land, when the atmosphere was so uncom¬ 
monly thick and hazy, that the dew on the horses’ bri¬ 
dles was remarkably clammy and unctuous. This me¬ 
teor was sometimes globular, then in the form of the 
flame of a candle, presently afterwards it spread itself 
so much as to involve the whole company in a pale harm¬ 
less light, and then it w'ould contract itself again, and 
suddenly disappear ; but, in less than a minute, it would 
become visible as before, and running along from one 
place to another with a swift progressive motion, would 
again expand itself, and cover a considerable space of 
ground. 

10. Of the aurora borealis, or northern 
LIGHTS. There have been various opinions and conjec¬ 
tures respecting the cause and properties of these extra¬ 
ordinary phaenomena ;f and the most probable opinion 
is, that they arise from exhalations, and are produced 
by a combustion of inflammable air, caused by electricity. 
This inflammable air is generated particularly between 
the tropics, by many natural operations, such as the 
putrefaction of animal and vegetable substances, volca¬ 
noes, &c. and being lighter than any other, ascends, 
to the upper regions of the atmosphere, and, by the mo- 


* Shaw’s Travels, page S63. 

t Philosophical Transactions. Nos. 305, 310, 320, SAT, 348, 349, 351 
352, 363, 365, S68, 376, 385, 395, 398, S99, 402, 410, 418, 431, a?nl 

IQQ ^ 1 



VAPOURS, FOGS, CLOUDS, &c. 


J19 


tlon of the earth, is urged towards the poles ; for it has 
been proved by experiments, that, whatever is lighter or 
swims on a fluid which revolves on an axis, is urged to¬ 
wards the extreme points of that axis hence, these in¬ 
flammable particles continually accumulate at the poles, 
and by meeting with heterogeneous matter, lake fire, and 
cause those luminous appearances frequently seen to¬ 
wards the polar regions.f 

In high latitudes the Aurorae Boreales appear with 
the greatest lustre, and extend over the greater paxt of 
the hemisphere, varying their colours from all the tints 
of yellow to the most obscure russet. J In the north¬ 
east parts of Siberia, Hudson’s Bay, &c. they are at¬ 
tended by a continued hissing and cracking noise through 
the air, similar to that produced by fire works.§ 

11. Of the RA.INBOW. The rainbow is the most 
beautiful meteor with which we are acquainted : it is 
never seen but in rainy wealher, where the sun illumi¬ 
nates the falling rain, and when the spectator turns his 
back to the sun. There are frequently two bows seen, 
the interior and exterior bow. The interior bow is the 
brightest, being formed by the’rays of light failing on the 
upper part of the drops of rain ; for a ray of light enter¬ 
ing the upper parts of a drop of rain will, by refraction, 
be thrown upon the inner part of the spherical surface 
of that drop, whence it will be reflected to the lower 
part of the drop, where, undergoing a second refraction, 


• See Mr. Kirwan’s account of the Aurora Borealis, Irish Phil. 
Transactions for 1TS8, page TO, Sic. 

t We have very few accounts of the Aurora Australia, or Southern 
Lights, owing perhaps to the want of observations on those remote 
parts of the globe, and a proper channel of information. Captain Cook, 
in his second voyage towards the south pole, says; “ (February tTth, 
1773,) W^e observed a beautiful phenomenon in the heavens, consisting 
of long columns of clear white light, shooting up from the heavens to 
the eastward, almost to the zenith, and gradually spreading over the 
whole southern part (*( the sky. Though these columns were in most 
respects similar to the Aurora Borealis, yet they seemed to differ from 
them in being always of a whitish colour. The stars were sometimes 
hid by, and sometimes faintly to he seen through, the substances of these 
Auroraj Australes. The sky was generally clear vvhen they appeared, 
and the air sharp and cold, the thermometer standing at the freezing 
point; the ship being in latititude 58° south.’^ 

I Dr. Rees^ New Cyclopaedia, word Vurora Borealis, 
i Philosophical Transactions, vol. Ixxiv. page 228. 



120 


VAPOURS, FOGS, CLOUDS, &c. 


it will be bent towards the eye of the spectator ; hence^ 
the rays whichfali upon the interior bow come to the eye 
after two refractions and one reflection, and the colours 
of this bow from the upper part are red, orange, yellow, 
green, blue, indigo, and violet. The exterior bow is 
formed by the rays of light falling on the lower parts of 
the drops of rain ; these rays, like the former, undergo 
two refractions, viz. one when they enter the drops, and 
another when they emerge from the drops to the eye ; 
hut they suffer two or more reflections in the interior 
surface of the drops ; hence, the colours of these rays 
are not so strong and well defined as those in the interior 
bow, and appear in an inverted order, viz. from the un¬ 
der part they are red, orange, yellow, green, blue, indi¬ 
go, and violet. To illustrate this by experiment, sus¬ 
pend a glass globe filled with water in the sun-shine, 
turn your back to the sun, and view the globe at such a 
distance that the part of it farthest from the sun may 
appear of a full red colour, then will the rays which come 
from the globe to the eye make an angle of 42 degrees 
with the sun’s direct rays ; and if the eye remain in the 
same position and another person lower the glass globe 
gradually, the orange, yellow, green, &c. colours, will 
appear in succession, as in the interior bow. Again, if 
the glass globe be elevated, so that the side nearest to 
the sun may appear red, the rays which come from the 
globe to the eye will make an angle of about 50 degrees ; 
then, if another person gradually raise the glass globe, 
while the spectator remains in the same position, the 
rays will successively change from red to orange, green, 
yellow, &c. as in the exterior bow. These observa¬ 
tions being understood, let dne (Plate IV. Fig. I.) rep¬ 
resent a drop of rain belonging to the interior bow, Sd 
a ray of light falling on the upper part of the drop at d ; 
instead of the ray continuing its direction towards F, it 
will be refracted or bent towards n, whence part of it 
(for some will pass through the drop)will be reflected to 
e, making the angle of incidence dnk equal to the angle 
of reflection enk; instead of continuing its direction 
from e towards /, it will, by emerging out of the water 
into the air, be again refracted to the eye at 0. But, as 


VAPOURS, FOGS, CLOUDS, &c. 


121 


this ray of light consists of a pencil* of rays, some of 
Mhich are more refrangiblef than others, the violet, 
which is the most refrangible, will proceed towards B, 
and the red, which is the least refrangible, wdll proceed 
towards O. Now, if the eye of the spectator be so pla¬ 
ced that the ray of light falling upon it has been once re¬ 
flected, and twice refracted, so that Oe shall make, with 
the solar ray Sd, an angle SmO of 4*2° 2',J he will 
see the red ray in the direction Gem; and if the eye be 
raised to B, so that Be shall make, with the solar ray Sd, 
an angle BFS of 40° 17', the violet ray will be seen in 
the direction BcF ; the red ray will appear the highest, 
the violet the lowest, and the rest in order, according to 
their different refraugibility, as in the interior bow (Fig. 
2. Plate IV.) for the drop of water descends from F to 
e. What has been observed of one drop of water, will 
be true in an infinite number of drops ; hence, the inte¬ 
rior bow is composed of a circular arch, whose breadth 
is Fe, proportional to the difference between the least 
and most refrangible rays. 

To explain the exterior bow. Let ctnd (Plate IV. 
Fig. 1.) represent a drop of rain, Sd a ray of light falb 
ing upon the under part of it at d ; instead of (his ray 
continuing its direction towards m, it will be refracted 
to n, whence part of it will pass through the drop, and 
the rest will be reflected to f ; at f a part of it will again 


* A pencil of rays is a portion of light of a conical form, diverging 
or proceeding from a point; or tending to a point, in which case the 
rays are said to converge. 

t Kefrangibility of the rays of light is their tendency to deviate 
from their natural course. Those rays which deviate most from their 
natural course, in passing out of one medium into another, are said to 
be the most refrangible ; and those which deviate the least from their 
natural course, are the least refrangible. Sir Isaac Newton, by experi¬ 
ment, found the red rays to be the least refrangible, and the violet 
rays the most; and those rays which are the least refrangible are like¬ 
wise the least refiexibie. 

I The sine of incidence and refraction of the least refrangible rays, 
out of water into air, is as 3 to 4, or as 81 to 108 ; and the most refran¬ 
gible, as 81 to 109. Emerson’s Optics, p. 92.—The same author at 
page 237, prob. xxvi. of his Optics, by the method of fluxions or incre¬ 
ments and using the numbers above, finds that the angle which the 
emergent ray makes with the incident ray, in the interior bow, is 42® 2' 
for the red, and 40’ 17' for the violet; and for the exterior bow, these 
angles are 50° 57', and 54° 7'. The investigations are here omitted, 
because they cannot be rendered intelligible to any persons but mathe¬ 
maticians. 


18 



122 


VAPOURS, FOGS, CLOUDS, &«. 


pass through (he drop, and the remainder will be reflec¬ 
ted to C ; then in emerging from the water into the air, 
instead of continuing the direction CZ, it will be refrac¬ 
ted from C to the eye at O. But as this ray of light, 
like that in the interior bow, consists of a pencil of rays 
of difierent refrangibility, the red, which is the least 
refrangible, will proceed towards A; and the violet, 
which is the most refrangible, will proceed towards O. 
Now, if the eye of the spectator be so placed that the 
ray of light falling upon it has been twice reflected, and 
twice refracted, so that Oo shall make with the solar 
ray So an angle SoO of 54° 7^ he will see the violet ray 
in the direction OcY ; and if the eye be raised to A, 
so that Ao shall make with the soIeu* ray So an angle 
So A of 50® 57', the red ray will be seen in the direction 
Acr ; the violet ray will appear the highest, and the 
red ray the lowest, and the rest in order according to 
their diflercnt refrangibility, as in the exterior bow 
(Plate IV. Fig. 2.) for the drop of water descends from 
H to d. The same observations apply to an infinite 
number of drops, as in the interior bow. 

Hence, if the sun were a point, the breadth of the 
exterior bow would be (54® 7'—50° 57'=) 3® 1 O', that 
of the interior bow (42° 2'—40° 17'=) 1° 46', and the 
distance between them (50° 57'—42° 2'=) 8° 55 ; but, 
as the mean diameter of the sun is about 32'2", the 
breadths of the bows must be increased by this quantity, 
and their distances diminished ; the breadth of the ex¬ 
terior bow will then be 3° 42', that of the interior bow 2° 
17', and their distances 8° 23'. The greatest semi-diame¬ 
ter of the interior bow wdll be (42° 2'-f 16', the sun^s 
semi-diameter=) 42° 18', and the least semi-diameter 
of the exterior bow (50® 57'—16' the sun’s semi-diame- 
ter=) 50° 41'. 

All rainbows are arches of equal circles, and conse¬ 
quently, are equally large, though we do not always see 
an equal quantity of them ; for the eye of a spectator 
is the vertex of a cone, and its circular base is the rain¬ 
bow, the semi-diameter of which (for the interior bow) 
iS the fixed quantity 42° 18, equal to the angle FOP; 
and as SF will, in all situations, be parallel to OP, and 
the angle SFO, equal to FOP, must be always equal to 
42° 18', it is evident that, as S rises, F and P will sink; 


VAPOURS, FOGS, CLOUDS, &c. 


123 


and when SF makes an angle of 42° 18', with the hori¬ 
zon, OF will coincide with OQ, and the interior bow 
will vanish ; hence, the interior bow cannot be seen if 
the sun’s altitude exceed 42° 18': again, as the point? 
rises, the point S will sink, and when OP coincides with 
OQ, SF will be parallel to the horizon (viz. the sun will 
be rising or setting) and the whole semi-diameter of the 
rainbow will appear, which is the greatest part of it that 
ever can be seen on level ground ; hence, half a rain¬ 
bow is the most that can be seen in such a situation : 
but if the observer be on the top of a high mountain, 
such as the Andes, with his back to the son, and if it 
rains in a valley before him, a whole rainbow may be 
seen, forming a complete circle. The above reasoning 
is equally applicable to the outer bow ; hence, as the 
sun rises, the bows sink; and, when his altitude exceeds 
42° 18', the interior bow cannot be seen, and, if it ex¬ 
ceed (54° 7'-f 16'=) 54° 23', the exterior bow cannot 
be seen. 


PART 11. 


THE ELEMENTARY PRINCIPLES OF ASTR0N0M;Y. 

CONTAINING, 

T. The Solar System, kc. 2. The nature of Comets; the Elongation.®, 
stationary and retrograde Appearances of the Planets; of the Fixed 
Stars; the Eclipses of the Sun and Moon, kc. 

CHAPTER I. 

Of the Solar System* {Plate IL Figure I.) 

THE solar system is so called because the sun is sup¬ 
posed to be placed in a certain point, termed the centre 
of the system, having all the planets revolving round him 
at different distances, and in different periods of time^ 
This is likewise called the Copernican system. 

1. OF THE SUN. 

The sun is situated near the centre of the orbits of all 
the planets, and revolves on its axis in 25 days, 14 
hours, 8 minutes. This revolution is determined from 
the motion of the spots on its surface, which first make 
their appearance on the eastern extremity, and then by 
degrees come forward towards the middle, and so pass 
on till they reach the western edge, and then disappear. 
When they have been absent for nearly the same period 
of time which they were visible, they appear again as at 
first, finishing their entire circuit in 27 days, 12 hours, 
20 minutes.* 


* M. Cassini determined the time which the sun takes to revolve on 
its axis thus; the time in which a spot returns to the same situation on 
the sun^s disc (determined from a series of accurate observations) is 27 d. 



THE SOLAR SYSTEM. 


125 


The sun is likewise agitated by a small motion round 
the centre of gravity of the solar system, occasioned by 
the various attractions of the surrounding planets ; but, 
as this centre of gravity is generally within the body of 
the sun,* * and can never be at the distance of more than 
the length of the solar diameter from the centre of that 
body, astronomers generally consider the sun as the cen¬ 
tre of the system, round which all the planets revolve; 
though in reality the centre of gravity of the sun and of 
all the planets is the centre of the world.f As the sun 
revolves on an axis, his figure is supposed not to be 
strictly in the form of a globe, but a little flatted at the 
poles ; and that his axis makes an angle of about eight 
degrees, J with a perpendicular to the plane of the earth’s 
orbit. As the sun’s apparent diameter is longer in De¬ 
cember than in June, it follows that the sun is nearer to 
the earth in our winter than it is in summer ; for the ap¬ 
parent magnitude of a distant body diminishes as the dis¬ 
tance increases. The mean apparent diameter of the sun 
is stated to be 32' 2" ; hence, taking the distance of the 
sun from the earth to be 95 millions of miles, as before 
determined,^ its real diameter will be 886149 miles; 
and, as the magnitudes of all spherical bodies are as the 


12 h.20 ra.; now the mean motion of the earth in that time is 27® V S'/ 
hence, S60® X ^27° 7' 8": 2T d. 12 h. 20 ra.:; 360° :25 d. 14 h. 8 m.; 
the time of rotation. 

* Sir Isaac Newton’s Princip Book iii. Prop. 11 and 12. 
t Newton’s Princip. Book iii. Prop. 12. Corol. 
i; Walker’s Familiar Philosophy. Lecture xi. p. 51G. 

J The semi»diameter of the earth has been determined at page 57, in 
the note, to be 5982 miles; and the distance of the earth from the sun 
is 25882.84 semi-diameters of the earth. Seo the note, page 62. Now, 
the apparent semi-diameter m n of the sun (Plate IV. Fig. 3.) is 
measured by the angle m o n=32' 2'' ; hence the angle o m 7i=the 
180°—32' 2" 

angle o n in --- 89® 43' 59" ; and on account of the dis- 

2 

tance of the sun from the earth, o w, oc, and o n may be considered as 


enual. Hence, 

Sine o 71 m 89° 43' 59".9.9999953 

Is to 23882.84 semi-diameters. 4.3780860 

As sine m o n 32' 2"... 7.9693152 

Is to 222 5388 semi-diameters.2..3474059 


Now, 222 5838 X ^-=886149.5016 miles, the diameter of the sun, 
the cube of which is divided by the cube of 7964, the diameter of the 
earth, gives 1377613 times the sun is larger than the earth. 








126 


THE SOLAR SYSTEM. 


-.vCubes'^ of their diameters, the magnitude of the sun will 
be ISrrblS times that of the earth ; the diameter of the 
earth being only r964 miles, the diameter of the sun is 
above one hundred and eleven times the diameter of the 
earth. 


II. OF MERCURY 5^. 

Mercury is the least of all the planets whose magni¬ 
tudes are accurately known, and the nearest to the sun. 
The inclination of its axis to the plane of its orbit, and 
the lime it takes to revolve on its axis, are unknown, 
consequently, the vicissitudes of its seasons, and the 
length of its day and night, are likewise unknown. Mer¬ 
cury is seen through a telescope sometimes in the form 
of a half moon, and sometimes a little more or less than 
half his disc is seen; hence, it is inferred, that he has the 
same phases as the moon, except that he never appears 
quite round, because his enlightened side is never turn¬ 
ed directly towards us, unless when he is so near the sun 
as to become invisible, by reason of the splendor of the 
sun’s rays. The enlightened side of this planet being 
always towards the sun, and his never appearing round, 
are evident proofs that he shines not by his own light; 
for, if he did, he would constantly appear round. 
The best observations of this planet are those made 
when he is seen on the sun’s disc, called his transit; for, 
in his lower conjunction, he sometimes passes before the 
sun, like a little spot, eclipsing a small part of the sun’s 
body, only observable with a telescope. That node 
from which Mercury ascends northward above the eclip- 
6c is in the fifteenth degree of Taurus ;f and, conse¬ 
quently, the opposite or descending node is in the fif¬ 
teenth degree of Scorpio. The earth is in the fifteenth 
degree of Taurus on the 6th of May, and in the fifteenth 
of Scorpio on the fourth of November; and when Mer¬ 
cury comes to either of his nodes at his inferior con¬ 
junction (viz. when he is between the earth and the sun) 


* Euclitl xii. and 18th. 

t The place of Mercury^s ascending node for 1750 was 15® 20' 43" 
in Taurus, and its variation in one hundred years is I® 12/ 10". Vhxcth 
Astronomy. 



THE SOLAR SYSTEM. 


127 


iie will pass over the sun’s disc, if il happen on or near 
the days above mentioned ; but in all other parts of his * 
orbit, he goes either above or below the sun, and conse¬ 
quently his conjunctions are invisible. 

Mercury performs his periodical revolution round the 
sun in 87 d. 23 h. 15 min. 43 sec. ; bis greatest elonga¬ 
tion is28” 20', distance from the sun 36814721* miles; 
the eccentricity of his orbit is estimated at one-fifth of 
his mean distance from the sun; his apparent diameter 


* The distance of Mercury, or any planet, from the sun, may be 
found by Kepler^s rule. Thus, the square of the time which the earth 
takes to revolvre round the sun, is to the cube of the mean distance of 
the earth from the sun, as the square of the time which any other planet 
takes to revolve round the sun, is to the cube of its mean distance; 
the cube-root of which will give the distance sought. Ob, tchick is 
shorterj divide the square of the time in which any planet revolves round 
the sun, by the square of the time in which the earth revolves round 
the sun, the cube-root of the quotient will give the relative distance of 
the planet from the sun. This relative distance multiplied by the mean 
distance of the earth from the sun, will give the mean distance of the 
planet from the sun. 

First for Mercury. The earth revolves round the sun in OS'* d. 5 h. 48 
in. 48 sec. ==31556928 sec. the square of w'hich is 995839704797184, a 
constant division for all the planets, and 23882.84, the distance of the 
earth from the sun in semi-diameters (see page 62, note) will be a con¬ 
stant multiplier. 87 d. 23 h. 15 m. 43 sec. =7600543 sec. the square of 
which is 57768253894849. This square divided by the former gives 
,0580096 nearly, the cube-root of which is 38710991, the distance of 
Mercury from the sun, supposing the distance of the earth from the 
sun to be an wmV. .38710991 X23882.84=9245.2841 distance of Mer¬ 
cury from th e sun in semi-diameters of the earth ; hence, 9245.2841 X 3 
982 radius of the earth, =36814721 miles, the mean distance of Mer¬ 
cury from the sun. 

The distance of the inferior planets from the sun may be found by 
their elongations. M. de la Lande hasfcalculated that, when Mercury 
is in his aphelion, and the earth in its perigee, the greatest elongation 
of Mercury is 28® 20'; but when Mercury is in his perihelion and the 
earth in its apogee, the greatest elongation is 17® 36'; the medium, 
therefore, is 22° 58'. Hence, in the triangle sev (Plate II. Fig. 2.) the 
angle sev=22° 58', the distance of the earth from the sun se=2S882 
.84 semi-diameters, and evs is a right angle. 

Radius, sine of 90° . . 10.0000000 

Is to SE =23882-84 . 4.3780860 

As sine of22° 58'. 9,5912823 

Is to 9318.976 semi-diameters . . . S.969S68S 

Hence, 9318976 X 3982=37108162 mile.s, the distance of Mercury from^ 
the sun by this method ; but an error of a few feconds in the elongation 
will make a considerable difference. 





J28 


THE SOLAR SYSTEM. 


11" ; hence, his real diameter is 3108 miles,* and his 
magnitude about one-sixteenth of the magnitude of the 
earth. 

Mercury emits a bright white light; he appears a lit¬ 
tle after sun-set, and again a little before sun-rise ; but, 
on account of his nearness to the sun, and the smallness 
of his magnitude, he is seldom seen. The light and heat 
which this planet receives from the sun, is about seven 
times greater than the light and heat which the earth 
receives.f The orbit of Mercury makes an angle of 
seven degrees with the ecliptic, and he revolves round 
the sun at the rate of upwards of one hundred and nine 
thousand miles per hour.J The manner in which the 


* The mean distance of the earth from the sun is seml-diam. 

and Mercury’s distance 9'i45.^i841 serni-diam. : tlie difference is 14637 
.55-'>9 semi-diam., the distance of Mercury from the earth; and, as the 
magnitudes of all bodies vary inversely as their distances, we have by 
the ruleof three inverse .4537.5559 : It": ; 23882 84: 6" .74179, the 
apparent diameter O Mercury, at a distance from the earth equal to 
that of the sun. Now the mean apparent diameter of the sun is 32' 2" 
and its real diameter 886149 miles ; hence, 32' 2" : 886149 m. : : 6" 
-74179 : 3108 miles of the diameter of .Mercury : and if the cube of the 
diameter of the earth be divided by the cube of the diameter of Mercu¬ 
ry, the quotient will be 16.8 times the magnitude of the earth exceeds 
that of Mercury. 

The diameter of Mercury might have been found exactly in the same 
manner as the diameter of the sun was found in the note page 125, 
using It" instead of 32'' 2", and 14637.5559 semi-diam. instead of 
23882.84 semi-diam. ; the result of 'the operation in this case will be 
78061 semi-diam. of the earth; hence, .78061 X 3982=3108 miles the 
diameter of Mercury exactly as above, it has been remarked at page 63, 
that the apparent diameters of the planets aro measured by a microme¬ 
ter, said to be iiivented by M Azout, a Frenchman ; but it appears, 
from the Philosophical Transactions, that it was invented by Mr. Gas¬ 
coigne, an Englishman. 

+ As the effects of light and heat are reciprocally proportional to the 
squares of the distances from the centre whence they are propagated, if 
you divide the square of the earth’s distance from the sun, by the square 
of Mercury’s distance from the siin, the quotient will shew the com¬ 
parative heat of Mercury to that of the earth. 

I This is found in the same manner as lor the earth at page 63. Thus 
if you double the distance of any planet from the sun, then multiply by 
S55, and divide the last product by 113, you obtain the circumference 
of the planet’s orbit in miles. This circumference, divided by the num¬ 
ber of hours in the planet’s year, will give the number of miles per 
Lour which that planet travels round the sun: a general rule for all the 
planets. Hence, 

The circumference of Mercury’s orbit will be found to be 231313733 
.717 miles; then 87 d. 23 h. 15' 43" ; 231313733 717 railea:: 1 h.; lO'ji 
61 miles Mercury travels per hour. 



THE SOLAR SYSTEM. 


129 


earth revolves round the sun has already been explain¬ 
ed, at page 61, and, as all the other planets move in a 
similar manner in elliptical orbits, having the sun in one 
of the foci, what has been observed respectingthe earth, 
will be equally applicable to all the planets. 

III. OF VENUS 9 . 

Venus is the brightest, and to appearance, the largest 
of all the planets;her light is distinguished from that of 
the other planets by its brilliancy and whiteness, which 
are so considerable, that, in a dusky place, she causes an 
object to cast a sensible shadow. Venus, when viewed 
through a telescope, appears to have all the phases of 
the moon, from the crescent to the enlightened hemi¬ 
sphere, though she is seldom seen perfectly round. Her 
illuminated part is constantly turned towards the sun ; 
hence, the convex part of her crescent is turned towards 
the east when she is a morning star, and towards the 
west when she is an evening star: for, when Venus is 
west of the sun, as seen from the earth, that is, when her 
longitude is less than the sun’s longitude, she rises before 
him in the morning, and is then called a morning star ; 
but when she is east of the sun, viz. when her longitude 
is greater than the sun’s longitude, she shines in the 
evening after the sun sets, and is then called an evening 
star. 

Venus is a morning star, or appears west of the. gun 
for about 290 days, and she is an evening star, or ap¬ 
pears east of the sun for nearly the same length of time, 
though she performs her whole revolution round the sun 
in 224 days 16 hours 49 minutes 10 seconds. A very 
natural question here may be asked, viz. Why Venus 
appears a longer time to the eastward or westward of 
the sun than the whole time of her entire revolution 
round him? This is easily answered by considering 
that while Venus is going round the sun, the earth is go¬ 
ing round him the same way, though slower than Venus, 
and therefore, the relative motion of Venus is slower than 
her absolute motion. 

Sometimes Venus is seen on the disc of the sun in 
the form of a dark round spot. These appearances 
happen but seldom, viz. they can happen only when 

19 


130 


THE SOLAR SYSTEM. 


Venus is between the earth and the sun, and when the 
earth is nearly in a line with one of the nodes of Ve¬ 
nus.* The last transit of Venus was in IfGQ, and 
there will not happen another of them till the year 1874. 
The time which this planet takes to revolve on its axis, 
and the inclination of its axis to the plane of its orbit, 
have been given by different astronomers ; but Dr. 
Herschel, from a long series of observations on this 
planet, published in the Philosophical Transactions for 
1793, concludes, that the time of this planet’s rotation 
on its axis is equally uncertain ; that its atmosphere is 
very considerable; that it has probably inequalities on its 
surface, but that it requires a better eye than his, or 
the assistance of better instruments than he is pos¬ 
sessed of, to discover any mountains. The apparent 
diameter of Venus is stated to be 58". 79 ; the eccen¬ 
tricity of her orbit 473100 miles ;f her greatest elon¬ 
gation 47° 48' ; her revolution round the sun is perform¬ 
ed in 224 d. 10 h. 49 m. 10 sec. J as before stated; and 
if her apparent diameter be taken as above, her true di¬ 
ameter will be^ 7498 miles, and her magnitude some- 


* The place of the ascending node of Venus for 1750 was 14® 26' 18" 
in Gemini, and its variation in 100 years is 51' 40". Vince’s Astronomy. 

t For, according to M. de la Lande, if the mean distance of the 
earth be 100000, the eccentricity of Venus will be 498 ; hence, when 
the distance is 95 millions of miles, the eccentricity will be 47S100 
miles. 

:}; The seconds in this time=t9414150, the square of which is 
.‘5T6909220222500, tlys divided by 9958^9704797184 (^^ee the note, 
page i2r,) gives .37348.%. &:c the cube root of which, is .7233511; 
this multiplied by 23882.84 produces 17275.678585 semi-diam. 
which multiplied by 3982=68791752 miles the distance of Venus from 
the sun. 

de la Lande has found the greatest elongations of Venus to be 
47° 48' and 44” 57'when insitnilar situations to Mercury, mentioned in 
the note to page 127; the medium is 46® 22' 30", using this angle and 
the very same calculation as in the notes pages 127 and 128, the dis 
tance of Venus from the sun w ill be found=17288.09 semi-diameters of 
the earth; hence, the distance woll be had=68841ir4 miles, astonish¬ 
ingly near to the distance found by Kepler’s rule, considering the great 
difference in the principles of calculation, and a strong proof of the 
truth of the Copernican system. 

i Here, (as in the note page 128,) 23882*84—17275.678585= 
6607.16145 semi-diameter distance of Venus from the earth; hence, in¬ 
versely, 6607.16145 : 58' .79 : ; 23882.84 : 16" .26419, and 32' 2" 

: 886 I 49 : : 16" .26419 : 7498 miles the diameter of Venus. Or by 
trigonometry, using the angle 58" .79, and distance 6607.16145, the 
result is 1.88314 ; X 3982=7498 miles. 



THE SOLAR SYSTEM. 


131 


thing less than that of the earth ; likewise her distance 
from the sun which will be found to be 68791752 miles. 

The light and heat which this planet receives from the 
sun, are about double to what the earth receives.^. The 
orbit of Venus makes an angle of 3° 23'35"wilh the 
ecliptic, and she revolves round the sun at the rate of 
upwards of eighty thousand miles per hour.| This 
planet, like Mercury, never departs from the sun : she 
is only visible a few hours in the morning before the sun 
rises, or in the evening after he sets ; an evident proof 
that the orbits of these planets are contained within the 
orbit of the earth, otherwise they would be seen in oppo¬ 
sition to the sun, or above the horizon at midnight. 

IV. OF THE EARTH, 0 AND ITS SATELLITE THE 
MOON. 3 

The figure and the magnitude of the earth have been 
already explained in Chapter III. Part I ; and its diur¬ 
nal and annual revolution round the sun, distance from 
the sun, seasons of the year, &c. have been shown in 
Chapter IV ; as it would be superfluous to repeat those 
particulars here, this chapter is confined entirely to the 
moon. 

The moon being the nearest celestial b.">dy to the 
earth, and next to the sun, the most resplendent in ap¬ 
pearance, has excited the attention of astronomers in all 
ages. The Hebrews, the Greeks, the Romans, and, in 
general, all the ancients, used to assemble at the time of 
new, or full moon, to discharge the duties of piety and 
gratitude for its manifold uses. The day being measur¬ 
ed by observing the time which the sun took in appa¬ 
rently moving from any meridian to the same again, so 
the month was measured by the number of days elapsed 
from new moon to new moon ; this month was supposed 
to be completed in thirty days ;J and when the motion 


* This is found by dividing the square of the earth’s distance from 
the sun by the square of the distance of Venus from the sun. 

t By the process mentioned in the note page ISO, the circumference 
of the orbit of Venus will be found to be 432231362.123 miles ; then, 
as 224 d. 16 h.49m. 10 sec. : 432231362.123 miles : ; 1 h. : 89149 
miles Venus travels per hour. 

if The Rev. Mr. Costard, in his History of Astronomy, supposes 
that the oldest measure of time (taken fiom the revolutions of the heav- 



132 


THE SOLAR SYSTEM, 


of the moon came to be compared with, and adjusted 
to, the apparent motion of the sun, twelve of these 
months were thought to correspond exactly with the 
sun’s annual course. The lunar month is of two sorts, 
periodical and synodical. A periodical month is the 
time in which the moon finishes her course round the 
earth, and consists of 27' days T hours 43 min. 5 sec¬ 
onds : and a synodical month is the time elapsed from 
new moon to new moon, and consists of 29 days 12 
hours 44 min. 3 seconds. The synodical month was 
probably the only one observed in the infancy of as¬ 
tronomy. 

The orbit of the moon is nearly elliptical, having the 
earth in one of its foci ; but the eccentricity of this 
ellipsis is variable, being the greatest when the line of 
the apsides is in the s^ zygies, for then the transverse 
axis of the moon’s orbit is lengthened; and the least 
when the transverse axis is in the quadratures, for then 
the conjugate axis is lengthened, and consequently, the 
orbit approaches nearer to a circle. The moon, in her 
revolution round the earth, would always describe the 
same ellipsis, were that revolution undisturbed by the 
action of the sun ; the principal axis of her orbit would 
remain at rest, and be always of the same quantity; her 
periodic times would all be equal, and the inclination of 
her orbit to the ecliptic and the place of her nodes 
would be invariable : but her motions being disturbed 
by the action of the sun, they become subject to so ma¬ 
ny irregularities, that to calculate the moon’s place truly, 
and to establish the elements of her theory, are almost 
insuperable difficulties. 

The orbit of the moon is inclined to the ecliptic in an 
angle, which is variable from 5° to 5° 18', consequently, 
it is inclined in an angle of 5° 9' at a medium. The mo- 


pnly bodies) was a month : and. after the length of the year was dis¬ 
covered, the ecliptic, and all other circles, were divided into 360 equal 
parts, called degrees, because 30 d.X 12=360 days, the length of the 
year. Hist, of Astr. p. 44. In an account of the Pelew Islands we are 
told that the inhabitants reckoned their time by months, and not by 
years: for, when the King entrusted his son to the care of Captain 
Wilson he inquired how many moons would elapse before he might 
expect the return of his son. The inhabitants of these islands were 
totally ignorant of the arts and sciences. 



THE SOLAR SYSTEM. 


134 


tion of the moon’s nodes, or places where her orbit cross¬ 
es the orbit ot the earth, is westward, or contrary to 
the order of the signs : this motion is likewise irregular, 
but by comparing together a great number of distant 
observations, the mean, annual retrograde motion is 
found to be about 19® 19' 44", so that the nodes make a 
complete retrograde revolution from any point of the 
ecliptic to the same again in about 18 years 228 days 9 
hours. The axis of the moon is almost perpendicular 
to the plane of the ecliptic, the angle being 88° 17', con¬ 
sequently, she has little or no diversity of seasons. The 
moon turns round her axis, from the sun to the sun again, 
in 29 days 12 hours 44 minutes 3 seconds, which is ex¬ 
actly the time that she takes to go round her orbit from 
new moon to new moon ; she, therefore, has constant¬ 
ly the same side turned towards the earth. This, how¬ 
ever, is subject to a small variation, called the libration* 
of the moon, so that she sometimes turns a little more of 
the one side of her face towards the earth, and sometimes 
a little more of the other, arising from her uniform mo¬ 
tion on her axis, and unequal motion of her orbit; this 
is called her libration in longitude. The moon likewise 
appears to have a kind of vacillating motion, which pre¬ 
sents to our view sometimes more, and sometimes less 
of the spots on her surface towards each pole ; this 
arises from the axis of the moon making an angle of a- 
bout 1° 43' with a perpendicular to the plane of the 
ecliptic ; and, as this axis maintains its parallelism dur¬ 
ing the moon’s revolution round the earth, it must neces¬ 
sarily change its situation to an observer on the earth; 
this is called the moon’s libration in latitude. 

While the moon revolves round the earth in an ellip¬ 
tical orbit, she likewise accompanies the earth in its ellip¬ 
tical orbit round the sun ; by this compound motion her 
path is every where concave towards the sun.f 


* A lunar globe was published a few years ago by Mr. Russel, which 
filiows, not only the libration of the moon in the most perfect manner, 
but is a complete picture of the mountains, pits, and shades, on her sur¬ 
face. 

t See M. Maclaurin’s account of Sir Isaac Newton’s discoveries, 
book iv chap. 5 ; Rowe’s Fluxions, second edition, page 225 ; Fergu¬ 
son’s Astronomy, octavo edition, article 266 ; or a treatise on Astrono? 
my, by Dr. Olinthus Gregory, article 458. 



134 


THE SOLAR SYSTEM. 


The moon, like the planets, is an opaque body, and 
shines entirely by light received from the sun, a portion 
of which is reflected to the earth. As the sun can on¬ 
ly enlighten one half of a spherical surface atoned, it fol¬ 
lows that, according to the situation of an observer, with 
respect to the illuminated part of the moon, be will see 
more or less of the light reflected from her surface. At 
the conjunction, or time of new moon, the moon is be¬ 
tween the earth and the sun, and, consequently, that 
side of the moon which is never seen from the earth is 
enlightened by the sun ; and that side which is con¬ 
stantly turned towards the earth is wholly in darkness.* 
Now, as the moon in her orbit exceeds the apparent 
motion of the sun by about 12° 11' in a day,f it follows 
that, about four days after the new moon, she will be 
seen in the evening a lit tie to the east of the sun, after he 
has descended below the western part of the horizon. 
A spectator will see the convex part of the moon to¬ 
wards the west, and the horns or cusps towards the east; 
or, if the observer live in north latitude, as he looks at 
(he moon the horns will appear to the left hand; for,if 
the line joining the cusps of the moon be bisected by a 
perpendicular passing through the enlightened part of 
(he moon, that perpendicular will point directly to the 
sun. As the moon continues her motion eastward, a 
greater portion of her surface towards the earth be¬ 
comes enlightened ; and when she is 90 degrees east¬ 
ward, of the sun, which will happen about 7^ days 
from the time of new moon, she will come to the meridi¬ 
an about 6 o^cIock in the evening, having the appear¬ 
ance of a bright semi-circle ; advancing still to the east¬ 
ward, she becomes more enlightened towards the earth, 
and at the end of about 14|days, she will come to the 
meridian at midnight, being diametrically opposite to 
(he sun; and, consequently, she appears a complete 
circle, or, it is said to be full moon. The earth is now 
between the sun and the moon, and that half of her sur¬ 
face which is constantly turned towards the earth, is 
wholly illuminated by the direct rays of the sun : whilst 


♦ Except the light which is reflected upon it from the earth, which 
we cannot perceive, 
t See the note page 74. 



THE SOLAR SYSTExM. 


135 


that half of her surface which is nercr seen from the 
earth is involved in darkness. The moon continuing 
her progress eastward, she becomes deficient on her 
western edge, and about 7^ days from the full moon she 
is again within 90 degrees of the sun, and appears a 
semi-circle with the convex side turned towards the sun; 
moving on still eastward, the deficiency on her western 
edge becomes greater, and she appears a crescent, with 
the convex side turned towards the east, and her cusps 
or horns turned towards the west; and about 14^ days 
from the full moon she has again overtaken the sun, this 
period being performed in 29 days 12 hours 44 minutes 
3 seconds, as has been observed before. Hence, from 
the new moon to the full moon, the phases are horned, 
half moon, and gibbous ; and, as the convex or well-de¬ 
fined side of the moon is always turned towards the sun, 
the horns or irregular side, will appear to the east, or to¬ 
wards the left hand of a spectator in north latitude. 
From the full moon to the change, the phases are gib¬ 
bous, half moon, and horned, the convex or well-defined 
side of her face will appear to the east, and her horns 
or irregular side towards the west, or to the right hand 
of a spectator. 

As the full moon always happens when the moon is di-- 
rectly opposite to the sun, all the full moons, incur win¬ 
ter, happen when the moon is on the north side of the 
equinoctial. The moon, while she passes from Aries to 
Libra, will be visible at the north pole, and invisible dur¬ 
ing her progress from Libra to Aries ; consequently, at 
the north pole, there is a fortnight’s moonlight and a 
fortnight’s darkness by turns. The same phenomena 
will happen at the south pole during the sun’s absence, 
in our summer. If the earth, the moon, and the sun, 
were all In the same plane, there would be an eclipse of 
the sun at every new moon (for then the moon is between 
the earth and the sun,) and there would be an eclipse of 
the moon at every full moon, at which time the earth is 
between the sun and the moon. Bui as the orbit of the 
moon crosses the orbit of the earth or ecliptic in two op¬ 
posite points, called the nodes ; it is evident that the 
moon is never in the ecliptic except when she is in one 
of these nodes ; an eclipse, therefore, can never happen 
unless the moon be in or near one of these nodes, at all 



136 


THE SOLAR SYSTEM. 


other times she is either above or below the orbit of the 
earth; and though the moon crosses each of these i.odes 
every month, yet if there should not be a new or full 
moon, at or near the time, there will be no eclipse. (See 
more of this subject in a succeeding chapter.) The in¬ 
fluence of the moon upon the waters of the ocean has al¬ 
ready been explained; and the nature of the harvest- 
moon will be shown amongst the problems of the globes. 

The moon^s greatest horizontal parallax is 61' 3*2", 
the least 54' 4", consequently the mean horizontal par¬ 
allax is"^ 57' 48" ; and her mean distance from the earth 
SSGSdff miles. The apparent diameter of the moon is 
variable according to her distance from the earth ; her 
mean apparent diameter is staled to be 31' 7" ;J hence, 
her real diameter is 2144 miles,§ and her magnitude 
about of the magnitude of the earth. The moon per¬ 
forms her revolution round the earth in 27 days 7 hours 
43 minutes 5 seconds, as has been observed before, con¬ 
sequently she travels at the rate of 112270 miles per hour 


• Dr. Hutton^a Matheraatical Diet, word Parallax. 

+ As in the note page 62. 

Sine of the angle PSO 65' 48" . . . • 8.2256S35 
Is to semi-diam. of the earth PO . . . 0.0000000 
As radius sine of 90°=sine OPS , , , 10.0000000 
Is to 59.47938 semi-diaraeters .... 1.7743665 
Hence, 59.47938 X 3882=236846.89 miles, distance of the moon from 
the earth. 

Vince’s Astronomy. 

0 As in the preceding notes say, inversely, 59.47938 semi>diameters: 
SI'7" ; : 23882.84 sem.: 4" .6497, the apparent diameter of the moon 
at a distance from the earth equal to that of the sun , hence, 32' 2" : 
886149:: 4" .6497 : 2143.8 miles the diameter of the moon Or, by 
trigonometry, the angle m O »i, (Plate IV. Fig. 3.)=31' 7", hence, 
180°—31' 7" 

Own =-=89° 59' 44" 26^'" 

2 

Sine of 89° 59'44", &c.= (sine of 90 nearly) . . . lODOOOOOO 


Is to 59.47938 semi'diameters. 1.7743665 

As sine 31' 7".• . 7.9567310 

Is to .53839 semi-diameters of the earth . . , . . 1.7310975 


And .53839 X 3982=2143.80, &c., miles the diameter of the moon. See 
the notes pages 124,135. If the cube of the earth’s diameter be divided 
by the cube of the moon’s diameter, the quotient will be 51.2 ; hence, 
the magnitude of the earth is upwards of fifty times that of the moon. 

11 For. by the note page 128 ; 113: 355 :: 236846.9 X 2:1488153.09 
miles circumference of the moon’s orbit; then 27 d. 7 h. 43 m. 5 sec.: 
1488153.09 ra.:: 1 h.; 2269.5 miles. 






THE SOLAR SYSTEM. 137 

round the earth, besides attending the earth in its annu¬ 
al journey round the sun. 

The surface of the moon is greatly diversified with 
inequalities, which through a telescope have the ap¬ 
pearance of hills and valleys. Astronomers have drawn 
the face of the moon as viewed through a telescope, dis¬ 
tinguishing the dark and shining parts by their proper 
shades and figures. Each of the spots on the moon 
has been marked by a numerical figure, serving as a re¬ 
ference to the proper name of the particular spot which 
it represents as Herschel’s volcano ; 1, Grimaldi; 2, 
Galileo, Sec ,; so that the several spots are named from 
the most noted astronomers, philosophers, and mathe¬ 
maticians. The best and most complete picture of the 
moon is that drawn on Mr. Russel’s lunar globe. 

Dr. Herschel informs us that, on the 19th of April, 
1787, he discovered three volcanoes in the dark part of 
the moon; two of them appeared nearly extinct, the 
third exhibited an actual eruption of fire, or luminous 
matter. On the subsequent night it appeared to burn 
with greater violence, and might be computed to be a- 
bout three miles in diameter. The eruption resembled 
a piece of burning charcoal, covered by a thin coat of 
white ashes : all the adjacent parts of the volcanic moun¬ 
tain were faintly illuminated by the eruption, and were 
gradually* more obscure at a greater distance from the 
crater. That the surface of the moon is indented with 
mountains and caverns, is evident from the irregularity 
of that part of her surface which is turned from the sun; 
for, if there were no parts of the moon higher than the 
rest, the light and dark parts of her disc^ at the time of 
the quadratures would be terminated by a perfectly 
straight line ; and at all other times the termination 
would be an elliptical line, convex towards the enlight¬ 
ened part of the moon in the first and fourth quarters, 
and concave in the second and third ; but, instead of 
these lines being regular and well defined when the 
moon is viewed through a telescope, they appear notch¬ 
ed and broken in innumerable places. It is rather sin¬ 
gular that the edge of the moon, which is always turned 


Vince’s Astronomy. 

20 



J38 


THE SOLAR ^STEM. 

• 

towards the sun, is regular and well defined, and at the 
lime of full moon no notches or indented parts are seen 
on her surface. In all situations of the moon, the eleva¬ 
ted parts are constantly found to cast a triangular shad¬ 
ow with its vertex turned from the sun; and, on the con¬ 
trary, the cavities are always dark on the side next the 
sun, and illuminated on the opposite side : these appear¬ 
ances are exactly conformable to what we observe of 
hills and valleys on the earth ; and even in the dark part 
of the moon’s disc, near the borders of the lucid sur¬ 
face, some minute specks have been seen, apparently 
enlightened by the sun’s rays; these shining spots are 
supposed to be the summits of high mountains,* which 
are illuminated by the sun, while the adjacent valleys 
nearer the enlightened part of the moon are entirely 
dark. 


* Supposing this to be the fact, astronomers have determined the 
height of •some of the lunar mountains. The method made use of by 
Kiccioli (though it gives the true result only at the time of the quadra¬ 
tures) is here explained, because it is much more simple than the gene¬ 
ral method given by Dr. Herschel in the Philosophical Transactions for 
1T80. liet ADB (Plate IV. Fig. 7.) be the disc or face of the moon at 
the time of the quadratures, ACBthe boundary of light and darkness ; 
MO a mountain in the dark part, the summit M of which is just begin¬ 
ning to be enlightened, by a ray of light SAM from the sun. Now, by 
means of a micrometer, the ratio of M A to AB may be determined ; 
and as AC is the half of AB, and MAC aright-angled triangle, by Eu¬ 
clid 1 and 47th\/.4L^-j- A iyi*=CM from which take CO=AC, and 
the remainder MO, is the height of the mountain. Riccioli observed 
the illuminated part of the mountain St. Catharine, on the fourth day af¬ 
ter the new moon to be distant from the illuminated part of the moon 
about one-sixteenth part of the moon’s diameter, viz. M A=one-sixteenth 
of AB, or one-eighth of AC ; now, if we take the moon’s diameter 2144 
miles, as we have before determined, the height of this mountain will be 

8y^ miles ! Galileo makes MA =t-20th of AB ; and Hevelius makes 
M A =1-26th of AB ; the former of these will give the height of the 
mountain 5j% miles, and the latter /iyV miles. Dr. Herschel thinks, 
“ I hat the heights of the lunar mountains are in general greatly over¬ 
rated, and that the generality of them do not exceed half a mile in their 
perpendicular elevation.” i)n the contrary, M. Schroeter, a learned 
astronomer of Lilienihal, in the duchy of Bremen, says, that there are 
mountains In the moon much higher than any on the earth, and men¬ 
tions one above a thousand toises higher than Chimboraco in South 
America. The same author has likewise lately published a new work 
on the heights of the mountains of Venus, some of which he makes up¬ 
wards of twenty-three thousand toises in height, which is above seven 
times the height of Chimboraco I 





THE SOLAR SYSTEM. 


139 


Whether the moon has an atmosphere or not, is a 
question that has long been controverted by various as¬ 
tronomers ; some endeavour to prove that the moon has 
neither an atmosphere, seas, nor lakes ; while others 
contend that she has all these in common with our earth, 
though her atmosphere is not so dense as ours. It can¬ 
not be expected in an introductory treatise, where gene¬ 
ral received truths only ought to be admitted, that we 
should enter into the discussion of a controverted ques¬ 
tion ; however, it may be proper to inform the student, 
that the advocates for an atmosphere, if we may be al¬ 
lowed to reason from analogy, have the advantage over 
those who contend that there is none. It is admitted on 
all hands, that the moon has mountains and valleys, like 
the earth, and appears nearly the same wilh respect to 
shape and the nature of her motions ; may we not then 
fairly infer that she is similar to the earth in other re¬ 
spects. 


V. OF MARS % , 

Mars appears of a dusky red colour, and though he is 
sometimes apparently as large as Venus, he never shines 
with so brilliant a light. From the dulness and ruddy 
appearance of this planet, it is conjectured that he is 
encompassed with a thick cloudy atmosphere, through 
which the redrays of his light penetrate more easily than 
the other rays. This being the first planet without the 
orbit of the earth, he exhibits to the spectator different 
appearances to Mercury and Venus. He is sometimes 
in conjunction with the sun, like Mercury and Venus, 
but was never known to transit the sun’s disc. Some¬ 
times he is directly opposite to the sun, that is, he comes 
to the meridian at midnight, or rises when the sun sets, 
and sets when the sun rises ; at this time he shines with 
the greatest lustre, being nearest to the earth. Mars, 
when viewed through a telescope, appears sometimes 
full and round, at others, gibbous, but never horned. 
The foregoing appearances clearly shew, that Mars 
moves in an orbit more distant from the sun than that of 
the earth. The apparent motion of this planet, like that 
of Mercury and Venus, is sometimes direct, or from east 
to west; at others retrograde, or front west to east; and 


140 


THE SOLAR SYSTEM. 


somelimes he appears stationary. Sometimes he rises 
before the sun, and is seen in the morning ; at others he 
sets afler the sun, and of course is seen in the evening. 
Mars revolves on his axis in 24 hours 39 minutes 22 sec¬ 
onds ; and his polar diameter is to his equatorial diameter 
as 15 to 16, according to Dr. Herschel; but Dr. Mask- 
elyne, who carefully observed this planet at the time of 
opposition, could perceive no difference between his ax¬ 
es. The inclination of the orbit of Mars to the plane of 
the ecliptic is 1° 5V ; the place ofhis ascending node a- 
bout 18° in Taurus;"^ his horizontal parallax is said to be 
23" 6 : he performs his revolution round the sun in 686 
days 23 hours 15 minutes 44 seconds ; and his apparent 
semi-diameter, at his nearest distance from the earth, is 
25" ; consequently his mean distance from the sun is 
i4490r630f miles; his diameter 4318 miles ; and his 
magnitude a little more, than l^th of that of the earth. J 
This planet travels round the sun at the rate of 55223 
miles per hour and the parallax of the earth’s annual 


^ The longitndie of the ascending node of Mars for the beginning of 
the year 1750 was 17° 38' *58" in Taurus, and its variation in 100 years 
is A6' 40". Vince’s Astronomy. 

t For. 686 days 23 hours l5min.A4 sec.=59S54t44 seconds, the 
square of which is 3522914409972736, this divided by 995839704797184 
the seconds in a year (see the note page 127) gives 3.537632. the 
cube root of which is 1.523716, the relative distance of Mars from the 
suji. Hence, 1.523716 X 23882.84=36390.6654 distance of Mars from the 
sun in semi-diam, of the earth, and 36390.6654X5982=144907629,6 
miles the mean distance of Mars from the sun. Now, if the horizontal 
parallax of Mars at the time of oppo.«ition be 23" .6 as stated by M. de 
la Caille, we have (see l^'iate lY- Fig. 6 ) 

Sine PSO^sine 23" .6. 6.0583927 

Is to PO ==; one semi-diameter - - - 0 0000000 
As radius sine of 90° 10.0000000 

Is to SO =8741.93 semi-diam. - - . 3 9416073 


Renee, the distance of Mars from the earth at the time of opposition is 
8741 93 of the earth’s semi-diameters; 8741.93: 25":: 2.3882.84 : 9" .15 
the apparent diameter of Mars if seen from the earth at a distance equal 
that of the sun ; then 32' 2": 886149 ; : 9" .15 : 4218 miles the diame¬ 
ter of Mars. 

:{; The cube of 7964, the diameter of the earth, is 505119057344: 
and the cube of 4218, the diameter of Mars is 75044648232; the quo¬ 
tient produced by dividing the former by the latter, is 6.73, viz. the 
magnitude of the earth is nearly seven times that of Mars. 

0 For, 113: 355 : ; 144907630 X 2: 910481569 miles the circumfer¬ 
ence of the orbit of Mars, and 686 days 23 h. 15 m. 44 sec.: 910481569 
pi.:: 1 h.: 55223 miles. 





THE SOLAR SYSTEM. 


141 


orbit, as seen from Mars, is about 41 degrees. As the 
distances of the interior planets from the sun are found 
by their elongations, so the distances of the exterior 
planets may be found by the parallax of the earth’s an¬ 
nual orbit.* 

Vl. OF THE NEW PLANETS, CERES, PALLAS, JUNO, AND 
VESTA. 

1. On the first of January 1801, M. Piazzi, Astrono¬ 
mer Royal at Palermo, in the island of Sicily, discover¬ 
ed a new planet between the orbits of Mars and Jupiter 
(generally called Ceres Ferdinandia, from the island in 
which it was discovered, and Ferdinand IV. King of the 
Two Sicilies.) The elements of the theory of this plan¬ 
et are at present very imperfectly known: it appears like 
a star of the eighth magnitude (consequently it is invisi¬ 
ble to the naked eye,) its distance from the sun is said 
to be about 2^ times that of the earth, andjts periodical 
revolutions nearly four years and eight months. This 
planet, called by some astronomers an asteroid, is not 
confined within the ancient limits of the zodiac. Its di¬ 
ameter, according to Dr. Herschel, is about 162 miles. 

2. On the 28th of March 1802, Dr. Olbers of Bre¬ 
men, while examining some of the stars near the new 
discovered planet, Ceres Ferdinandia, perceived a star 
of the seventh magnitude, situated near the northern 
wing of the constellation Virgo, which had the appear¬ 
ance of a planet. By continuing his observations, ho 


» In Plate IV. Fig. 8. let S represent the sun, E the earth, and M 
Mars; now, as the earth moves quicker in its orbit than Mars, the 
planet Mars will appear to go backward Avhen the earth passes it. 
Thus, when the earth is at E, Mars will appear among the fixed stars 
at in ; but as the earth passes from E to e, Mars will appear to go from 
to ?i, though he is in reality travelling the same way as the earth 
from M to X) The place m where Mars is seen from the earth among 
the fixed stars, is called his Geocentric place, but the place P, where he 
would be seen from the sun, is called his Heliccenti ic uiace, and the 
arc wiP, which is the difference between his apparent and true place, is 
called the Parallax of the earth’s annual orbit Now as this angle may 
be determined from observation, and is known to be about ; in the 
right angled triangle SEM. we have given SE="iS882.84 semi-diame¬ 
ters, the distance of the earth from the sun, the angle SME measured 
by the arc m P =41®, to find SM=36403.49 semi-diameters of the earth, 
the distance of Mars from the sun. 



142 


THE SOLAR SYSTEM. 


soon discovered it to be a new planet, to which he gave 
the name of Pallas, As the theory of the various phe¬ 
nomena ot this planet is less known even lhan that of 
Ceres Ferdinandia, the accounts of its magnitude, dis¬ 
tance, and the time of its periodical revolution round the 
sun, must be very imperfect. Its distance from the sun, 
and the time of its revolution, are slated to be nearly the 
same as those of Ceres Ferdinandia, and its diameter a- 
bout 95 miles. 

3. On the 1st of September 1804, Mr. Harding, of 
Lilienthal in the duchy of Bremen, discovered the plan¬ 
et Juno. It appears like a star of the eighth magni¬ 
tude : the Planets or Asteroids, Ceres, Pallas, and Juno, 
are all so nearly at equal distances from the sun, that it 
is not yet decided with certainty, which of the three is 
nearest, or the most remote. 

4. On the 29th of March 1807, at 21 m. past 8. mean 
time. Dr. Olbers discovered a fourth new planet called 
Vesta; its right ascension at that time was 184° 8’ and 
its declination 11° 47' N. It is apparently about the 
same distance from the sun as the three already men¬ 
tioned. In size it appears like a star of the fifth magni¬ 
tude. 

VII, OF JUPITER , AND HIS SATELLITES, &c. 

Jupiter is the largest of all the planets, and, notwith¬ 
standing his great distance from the sun and the earth, 
he appears to the naked eye almost as large as Venus, 
though his light is something less brilliant. Jupiter, 
when in opposition to the sun (that is, when he comes to 
the meridian at rnid-night, or rises when the sun sets, 
and sets when the sun rises,) is much nearer to the earth 
than he is a little before and after his conjunction with 
the sun ; hence, at the time of opposition, he appears lar¬ 
ger and more luminous than at other times. When the 
longitude of Jupiter is less than that of the sun, he will 
be a morning star, and appear in the east before the sun 
rises, but when his longitude is greater than the sun’s 
longitude, he will be an evening star, and appear in the 
west after the sun sets. Jupiter revolves on his axis in 9 
hours 56 minutes, which is the length of his day ; but as 
his axis is nearly perpendicular to the plane of his orbit. 


THE SOLAR SYSTEM. 


143 


he has no diversity of seasons. Jupiter is surrounded 
by faint substances, called zones or belts ; which from 
their frequent changes in number and situation, are gen¬ 
erally supposed to consist of clouds. One or more dark 
spots frequently appear between the belts; and when a 
belt disappears, the contiguous spots disappear likewise. 
The time of the rotation of the different spots is varia¬ 
ble, being less by six minutes near the equator than near 
the poles. Dr. Herschel has determined, that not only 
the times of rotation of the different spots vary, but that 
the time of rotation of the same spot (between the 25th 
of February 1778 and the 12th of April) varied from 
9 hours 55 minutes 20 seconds, to 9 hours 51 minutes 35 
seconds. 

The inclination of the orbit of Jupiter to the plane of 
the ecliptic is 1° 18' 50" ; the place of his ascending 
node about 8 degrees in Cancer and he performs his 
revolution round the sun in 4330 days 14 h. 27. m. 11 
sec. moving at the rate of 29894 miles per hour, his 
mean distance from the sun being 494499108 miles.f Ju¬ 
piter at his mean distance from the earth, at the time of 
opposition, subtends an angle of 46", hence, his real di¬ 
ameter is 89069J miles ; and his magnitude 1400 times 
that of the earth.|| The light and heat which Jupiter 


* The place of Jupiter’s ascending node for the beginning of the year 
1750 was 7® 55' 32" in Cancer, and its variation in 100 years is 59' SO". 
Vince’s Astronomy. 

t For 4330 days 14 hours 27 minutes It seconds, =374164031 sec¬ 
onds, the square of which is 139978722094168961, this divided by 9958 
39704797184, the square of the seconds in a year (see the note page i27) 
gives 140.5835913, the cube root of v hich is 5.1997, the relative dis¬ 
tance of Jupiter from the sun. Hence, 23882-84 X 5.1997=124183.60 
3148 distance of Jupiter from the sun in serai-diameters of the earth ; 
and 124183.603148 X-982=494499107.7 miles, the mean distance of 
Jupiter from the sun. 

Now, (by the note page 128) tlS :S55 ;: 494499107.7 X 2 : 310702 
9791 miles, the circumference of the orbit of .Tupiter, and 4330 d. 14 h. 
27 ra. tl sec. : 3107029791 :: 1 h. : 29894 miles. 

^ 494499108—95-01468 miles the distance of the earth from the sun, 
=399397640 distance of the earth from Jupiter. Now, by the rule of 
three inversely, 399397640 ; 46":: 95101468 : 193" .1862, the appar¬ 
ent diameter of Jupiter at a distance from the earth equal to that of 
the sun. Hence, (as in the note page 128) 32' 2": 886149 ;: i93" .18 
62: 89069.5 rniie.s. the dianu ter cf Jupiter. 

II For, if the cube of the diameter of Jupiter be divided by the cube 
of the diameter of the earth, the quotient will be 1398.9=1400 nearly. 



144 


THE SOLAR SYSTEM. 


recelv'^es from the sun is about of the light and heat 
which the earth receives.* 

On account of the great magnitude of Jupiter, and 
his quick revolution on his axis, he is considerably more 
flatted at the poles than the earth is. The ratio between 
his polar and equatorial diameters has been differently 
stated by different astronomers ; Dr. Pound makes it as 
12 to 13; Mr. Short as 13 to 14 ; Dr. Bradley as 12 | to 
13|; and Sir Isaac Newton (by theory) as 94 to 104 . 

Of the Satellites of Jupiter. 

Jupiter is attended by four satellites or moons, each 
of which revolves round him in a manner similar to that 
of the moon round the earth. The times of their peri¬ 
odical revolutions round Jupiter, and their respective 
distances from his centre, are given in the following ta¬ 
ble.f 


Satellites. 

Periodical revolution. 

Distance from 
Jupiter in semi¬ 
diameters. 

Distance from 
Jupiter in En¬ 
glish miles. 

I. 

d. h. m. sec. 
1 . 18.2r . 33 

5.67 

252511 

II. 

3 . 13 . 13 . 42 

9.00 

400810 

III. 

7 . 3 .42 . 33 

14.38 

640406 

IV. 

16 . 16 . 32 . 08 

25.30 

1126r23 


The satellites of Jupiter are invisible to the naked 
eye; they were first discovered by Galileo, the invent- 


* If the square of the mean distance of Jupiter from the sun be divi¬ 
ded by the square of the mean distance of the earth from the sun, the 
quotient will be 27. 

t The second and third columns in the above table are copied from 
M. de la Lande, and the fourth is found by multiplying the numbers 
in the third column by 44534.5 being the half of 89069, the diameter of 
Jupiter. The distances of the satellites from the centre of Jupiter may 
be found at the time of their greatest elongations, by measuna 2 r their 
distances from the centre of Jupiter, and also the diameter of Jupiter, 
with a micrometer. Then say, as the apparent diameter of Jupiter (by 
the micrometer) is to his real diameter, so is the apparent distance of 
the satellite to its real distance. Or, having determined the periodical 
times of the satellites, aud the distance of one of them from the sun, the 
distances of all the rest may be found by Kepler’s rule, as in page 127. 









THE SOLAR SYSTEM. 


145 


or of telescopes, in the year 1610. This was an important 
discovery; for as these satellites revolve round J upiter 
in the same direction which Jupiter revolves round the 
sun, they are frequently eclipsed by his shadow, and af¬ 
ford an excellent method of finding the true longitudes 
of places on the land. To these eclipses we likewise 
owe the discovery of the progressive motion of light, and 
hence, the aberration of the fixed stars. 

The satellites of Jupiter do not revolve round him in 
the same plane, neither are their nodes in the same 
place. These satellites appear of different magnitudes 
Und brightness; the fourth generally appears the smallest, 
but sometimes the largest, and the apparent diameter of 
its shadow on Jupiter is sometimes greater than the sa¬ 
tellite. M. Cassini and Mr. Pound supposed that the 
satellites of Jupiter revolve on their axes ; and Dr. Her- 
schel has discovere.d, that they revolve about their axes 
in the time in which they respectively revolve about Ju¬ 
piter. 

The first satellite is the most important of the four, 
from its numerous eclipses. The times of the eclipses 
of the satellites of Jupiter are calculated for the meri¬ 
dian of Greenwich, and inserted in the 3d page of the 
Nautical Almanac for every month, and their configura¬ 
tions or appearances with respect to Jupiter, are insert¬ 
ed in page 12. As the earth turns on its axis from west 
to east at the rate of 15 degrees in an hour, or one de¬ 
gree in four minutes of time, a person, one degree west¬ 
ward of Greenwich, will observe the emersion or immer¬ 
sion of any one of the satellites of Jupiter four minutes 
later than the time mentioned in the Nautical Almanac ; 
and, if he be one degree eastward of Greenwich, the e- 
clipse will happen four minutes sooner at his place of 
observation than at Greenwich. These eclipses must be 
observed with a good telescope and a pendulum clock 
which beats seconds or half seconds. 

The configurations of the satellites of Jupiter at nine 
o’clock at night, in the month of March, and in the year 
1813, are given in the 12th page of the Nautical Alma¬ 
nac as in the following page ; an explanation of which 
will render the 12th page of that work intelligible to a 
young student for any other year and month. 


146 


THE SOLAR SYSTEM. 


10. 

, .4 .3 .-2 ^ 

1* O 

11. 

^ 2 6 3 

12. 

1. ® 3(5 4 

13. 

.2 ^ .1^ .4 

18. 

1.0 o 

19. 

2*4# j O 

20. 

4." O •• 3. 


On the tenth day of the month, given above, the first 
satellite is eclipsed at nine at night ; the second, third 
and fourth satellites are on the left hand of Jupiter, and 
in north latitude. When a satellite has north latitude, 
that is, when it is above the orbit of Jupiter, it is mark¬ 
ed with a point on the left hand as .4 .3 .2. 

On the eleventh day of the month, at the same hour, 
the first and fourth satellites are on the right hand of Ju¬ 
piter, and in north latitude, the second and third are al¬ 
so on the right hand, and in conjunction, or appear as 
one. 

On the twelfth day, the second satellite will be eclip¬ 
sed, the first will be on the left hand, in south latitude ; 
and the third and fourth on the right hand, in conjunc¬ 
tion. 

When a satellite has south latitude, that is, when it is 
below the orbit of Jupiter, it is marked with a point on 
the right hand, as 1., 3., 4.,&c. 

On the eighteenth day, the first satellite will appear 
like a bright spot on the disc of Jupiter ; the second and 
third will be on the right hand in north latitude, and the 
fourth on the right hand in south latitude. 

On the nineteenth day, the second and fourth satel¬ 
lites will be eclipsed ; the first satellite will appear on the 
left hand in south latitude, and the third on the right 
hand in north latitude. 










THE SOLAR SYSTEM. 


147 


By observations on the satellites of Jupiter the pro¬ 
gressive motion of light was discovered ; for it has been 
found by repealed experiments, that when the earth is 
exactly between Jupiter and the sun, the eclipses of Ju¬ 
piter’s satellites are seen minutes sooner than the 
time predicted* by calculating from astronomical tables, 
truly constructed ; and when the earth is nearly in the 
opposite point of its orbit, these eclipses happen about 
8i minutes later than the time predicted; hence, it is in¬ 
ferred, that light takes up about 16| minutes of time to 
pass over a space equal to the diameter of the earth’s an¬ 
nual orbit, which is 190 millions of miles, or double the 
distance of the earth from the sun : for if the effects of 
light were instantaneous, the eclipses of the satellites 
would, in all situations of the earth in its orbit, happen 
exactly at the time predicted by calculation. 

VIII. OF SATURN I 2 , HIS SATELLITES AND RING. 

Saturn shines with a pale, feeble light, being the far¬ 
thest from the sun of any of the planets that are visible 
without a telescope. This planet when viewed through 
a good telescope, always engages the attention of the 
young astronomer by the singularify of its appearance. 
It is surrounded by an interior and exterior ring, beyond 
which are seven satellites or moons, all, except one, in 
the same plane with the rings. These rings and satel¬ 
lites are all opaque and dense bodies, like that of Sa¬ 
turn, and shine only by the light which they receive 
from the sun. The disc of Saturn is likewise crossed 
by obscure zones or belts, like those of Jupiter, which 
vary in their figure according to the direction of the 
rings. Saturn performs his revolution round the sun in 
ior.59 days 1 hour 51 minutes 11 seconds; hence, his 
mean distance from the sun is 907089032 miles and 
his progressive motion in his orbit is 22072 miles per 
hour. 


* For 107r>9 d. 1. 51 m. tl sec.=9!£9584S71 seconds, the square of 
which is 864126916890601441, this divided by 995839704797184, the 
square of the seconds in a year (see the note page 127) gives 867.7369 



MB 


IHE SOLAR SYSTEM. 


The inciination of the orbit of Saturn to the plane of 
the ecliptic is said to be 2° 29' 50", and the place of his 
ascending node about 21 degrees in Cancer.* * 

Saturn at his mean distance from the earth; subtends 
an angle of 20"; hence, his real diameter is TOfSOf miles, 
and his magnitude 966j times that of the earth. The 
light and heat which this planet receives from the sun is 
about part of the light and heat which the earth re¬ 
ceives.§ 

According to Dr. Herschel, Saturn revolves on his 
axis from west to east in 10 hours 16 minutes 2 seconds, 
and this axis is perpendicular to the plane of his ring. 
The equatorial diameter of Saturn, viz. the diameter in 
the direction of the ring, is to the polar diameter, viz. 
the axis, as 11 to 10. 

OF THE SATELLITES OF SATURN. 

Saturn is attended by seven moons: the fourth was 
discovered by Hu_ygens, a Dutch Mathematician, in the 
year 1655. The first, second, third, and fifth,were dis¬ 
covered at different times, between the years 1671 and 
1685, by Cassini, a celebrated Italian astronomer. The 
sixth and seventh satellites were discovered by Dr. 
Herschel in the years 1787 and 1789. The two satel- 


58 the cube root of which is 9.538118, the relative distance of Saturn 
from the sun. Hence, 23882.84 X 9.538118=227797.34609512, dis¬ 
tance of Saturn from the sun in semi-diameters of the earth ; and 227797 
•3460^512 X ^982=907089032.15 miles, the mean distance of Saturn 
from the sun. 113 : 355 : : 907089032 X 2; 5699408962.1238 miles, 
circumference of the orbit of Saturn. Then, 

10759 d. J h. 55 m. 11 sec.: 5699408962 miles : ; 1 h. : 22072 miles, 
which Saturn moves per hour in his orbit. 

* The place ot Saturn’s ascending node for the beginning of the year 
1750, was 21° 32' 22" in Cancer, and its variation in 100 years is 55' 
SO". Vince’s Astronomv. 

t 907989032--95101468 miles, the distance of the earth from the sun, 
=811987564 miles, distance of the earth from Jupiter. Now, inversely, 
811987564:20": : 95101468 : 170" .762, the apparent diameter of Sa¬ 
turn at a distance from the earth equal to that of the sun (by the note 
page 128 ;) 32' 2" : 886149 :: 170" .762: 78730 miles, the diameter of 
Saturn. 

Found by dividing the cube of the diameter of Saturn, by the cube 
of the diameter of the earth. 

$ Found by dividing the square of the mean distance of Saturn from 
the sun, by the square of the earth’s mean distance from the sun. 



THE SOLAR SYSTEM. 


149 


lites discovered by Dr. Herschel are nearer to Saturn 
than the other five, and therefore, should be called the 
first and second ; but to distinguish them from the other 
satellites, and to prevent confusion in referring to former 
observations, they are called the sixth and seventh sa¬ 
tellites. The seventh satellite, which is nearest to Sa¬ 
turn, was discovered a short time after the sixth. In 
the following table, the satellites are arranged according 
to their respective distances from Saturn, and the Roman 
figures in the left hand column show the number of the 
satellite. The figures between the parentheses show 
the order in which thej ought to be numbered. 


Satellites. 

Periodical revolution. 

Distance from 
Saturn in semi¬ 
diameters. 

Distance from 
Saturn in Eng¬ 
lish miles. 

VII. (1) 

d. h. m. sec 

0 . 22 , 37.23 

2^ 


111534 

VI. (2) 

1 . 8 . 53 . 9 



139964 

I. (3) 

1 . 21 . 18.27 

4| 

P 

172222 

II. (4) 

2 . 17.44 . 51 

H 


216507 

III. (5) 

4 . 12.25 . 11 

8 

o § 

314920 

IV. (6) 

15 . 22.41 . 16 

18 

o* a 

708570 

V. {7) 

79 . 7 . 53.43 

J4 , 


2125710 


The first, second, third, and fourth satellites, as well 
as the sixth and seventh, are all nearly in the same plane 
with Saturn’s ring, and are inclined to the orbit of Sa¬ 
turn in an angle of about 30 degrees; but the orbit of 
the fifth satellite is said to make an angle of 15 degrees 
with the plane of Saturn’s ring. Sir Isaac Newton con¬ 
jectured* that the fifth satellite of Saturn revolved 
round its axis, in the same time that it revolved round 
Saturn ; and the truth of his opinion has been verified by 
the observations of Dr. Herschel. 

OF SATURN'S RING. 

The ring of Saturn is a thin, broad, and opaque cir¬ 
cular arch, surrounding the body of the planet without 


* Principia, Book III. Prop.xvii. 











150 


THE SOLAR SYSTEM. 


touching it, like the wooden horizon of an artificial globe* 
If the equator of the artificial globe be made to coincide 
with the horizon, and the globe be turned on its axis 
from west to east, its motion will represent that of Sa¬ 
turn on its axis, and the wooden horizon will represent 
the ring, especially if it be supposed a little more dis¬ 
tant from the globe. The ring of Saturn was first dis¬ 
covered by Huygens ; and when viewed through a good 
telescope, appears double. Dr. Herschel says, that 
Saturn is encompassed by two concentric rings, of the 


following dimensions. 

Miles. 

Inner diameter of the smaller ring - - 146345 

Outside diameter of ditto - . - 184393 

Inner diameter of the larger ring - - 190248 

Outside diameter of ditto - - - 204883 

Breadth of the inner ring - - - 20000 

Breadth of the outer ring - - - 7200 

Breadth of the vacant space, or dark zone between 

the rings 2839 


The ring of Saturn revolves round the axis of Saturn, 
and in a plane coincident with the plane of his equator, 
in 10 hours 32 min. 15. 4 sec. The ring being a circle, 
appears elliptical, from its oblique position : and it ap¬ 
pears most open when Saturn’s longitude is about 2 
signs 18 degrees, or 8 signs 17 degrees. There have 
been various conjectures relative to the nature and pro¬ 
perties of this ring. 

IX. OF THE GEORGIUM SIDES, OR HERSCHEL H, AND 
HIS SATELLITES. 

The Georgian is the remotest of all the known planets 
belonging to the solar system ; it was discovered at Bath 
by Dr. Herschel on the 13th of March, 1781. This 
planet is called by the English the Georgium Sidus, or 
Georgian, a name by which it is distinguished in the 
Nautical Almanac. It is frequenily called by foreign¬ 
ers, Herschel, in honour of the discoverer. The royal 
academy of Prussia, and some others, called it Ouranus, 
because the other planets are riasned from such heathen 
deities as were relatives ; thus, Ouranus was the father 



THE SOLAR SYSTEM. 


151 


of Saturn, Saturn the father of Jupiter, Jupiter the fath¬ 
er of Mars, &c. This planet, when viewed through a tel¬ 
escope of a small magnifying power, appears like a star 
of between the 6th and Tth magnitude. In a very fine 
clear night, in the absence of the moon, it may be per¬ 
ceived by a good eye, without a telescope. Though the 
Georgium Sidus was not known to be a planet till the 
time of Dr. Herschel, yet astronomers generally believe 
that it has been seen long before his time, and consider¬ 
ed as a fixed star.* 

In so recent a discovery of a planet at such an im¬ 
mense distance, the theory of its magnitude, motion, &c. 
must be in some degree imperfect. Its periodical revo¬ 
lution round the sun is said to be performed in 30445-*^ 
days, or upwards of 83 years : the ratio of its diame¬ 
ter to that of the earth, is as 4.32 to 1; consequently, its 
magnitude is upwards of eighty times that of the earth. 
If the periodical revolution of the Georgian, as above,, 
be truly ascertained, its distance from the sun may be 
determined by Kepler’s rule, as for the other planets. 

The Georgian planet is attended by six satellites; 
their periodical revolutions and times of discovery are 
as follow: 




d. h. m. 

s. 

I. or nearest, revolves in 5 21 25 

0, discovered in 1798. 

II. 

- 

. 8 17 1 19, discovered in 1787. 

III. - 

- 

- 10 23 4 

0, discovered in 1798. 

IV. - 

- 

13 11 5 

1|^, discovered in 1787. 

V. 

- 

- 38 1 49 

0, discovered in 1798. 

VI. - 

- 

- 107 16 40 

0, discovered in 1798. 


All these satellites were discovered by Dr. Herschel; 
their orbits are said to be nearly perpendicular to the 
ecliptic, and what is more singular, they perform their 


According to F. de Zach^s account of this planet, in the Memoirs 
of the Brussel’s Academy. 1785, there were then in the library of the 
Prince of Orange, four observations of this planet considered as a star, 
in a catalogue of observations writen by Tycho Brahe ; but, as Tycho 
was not acquainted with the use of t« lescopes, some writers contend that 
he could not see it; ^^bile others maintain that, as he has marked stars 
which are not greater than this planet, he might certainly have seen it. 
This planet was likewise seen by Professor Mayer of Gottingen, in the 
year 1756, being the 964tli star of his catalogue. 



152 


THE ELONGATIONS, &o. 


revolutions round the Georgian planet in a retrograde 
order, viz. contrary to the order of the signs. 

CHAP. II. 

On the Nature of Comets ; the Elongations, Stationa- 
ry and Retrograde appearances of the Planets ; of 
the Fixed Stars ; and the Eclipses of the Sun and 
Moon, 


I. ON COMETS. 

THOUGH the primary planets already described, 
and their satellites, are considered as the whole of the 
regular bodies which form the solar system, yet that sys- 
ted is sometimes visited by other bodies, called comets, 
which are supposed to move round the sun in elliptical 
orbits. These orbits are supposed to have the sun in 
one foci, like the planets; and to be so very eccentric, 
that the comet becomes invisible when in that part of its 
orbit which is the farthest from the sun. It is extreme¬ 
ly difficult to determine the elliptic orbit of a comet, 
with any degree of accuracy, by calculation ; for, if the 
orbit be very eccentric, a small error in the observation 
will change the computed orbit into a parabola or hy¬ 
perbola; and from the thickness and inequality of the 
atmosphere with which a comet is surrounded, telescop¬ 
ic observations on them are always liable to error. 
Hence, the theory of the orbits, motions, &c. of comets, 
is very imperfect; and though many volumes have 
been written on the subject,*' they are chiefly|founded on 
conjecture. The unexpected appearance of the comet 
in 180r, fully confirms the assertion, and will doubtless 
give rise to a variety of new calculations, and newhypo- 


* The latest writings on the subject of comets are M. Pingr^’s Cometo- 
graphie, in 2 vols. 4 to. and Sir Henry Englefield’s work, entitled, “On 
the Determination of the Orbits of Comets.*’ A well written article 
on Comets may be seen in Dr. Rees* New Cyclopedia, together with 
the elements of ninety-seven of them, and the names of the authors whv 
have calculated their orbits. 



THE ELONGATIONS, &c. 153 

theses, which like former ones, for want of sufficient da¬ 
ta, will disappoint the expectations of succeeding astron¬ 
omers. The comets. Sir Isaac Newton* observes, are 
compact, solid, and durable bodies, or a kind of planets 
which move in very oblique and eccentric orbits every 
way with the greatest freedom, and preserve their mo¬ 
tions for an exceeding long time, even where contrary 
to the course of the planets. Their tail is a very thin 
and slender vapour, emitted by the head or nucleus of 
the comet, ignited or heated by the sun. 

II. OF THE ELONGATIONS, &c. OF THE INTERIOR 
PLANETS. 

LetT, E, c, (Plate IV. Fig. 8.) represent the orbit of 
the earth ; a, w, v, x,/, g*, h, the orbit of an interior plan¬ 
et, as Mercury or Venus, and S the sun. 

Let T represent the earth, S the sun, and a Venus 
at the time of her inferior conjunction ; at this time she 
will disappear like the new moon, because her dark side 
will be turned towards the earth. While Venus moves 
from a towards w she appears to the westward of the 
sun, and becomes gradually more and more enlightened 
(having all the different phases of the moon). When 
she arrives at v, her greatest elongation, she appears 
half enlightened, like the moon in her first quarter; at 
this time she shines very bright.f From her inferior to 
her superior conjunction, viz. from her situation in that 
part of her orbit which is directly between the earth and 
the sun, as at a, to her situation in that part of her orbit 
in which the sun is between her and the earth ; she rises 
before the sun in the morning, and is called a morning 
star. From her superior to her inferior conjunction she 
shines in the evening, after the sun sets, and is then call¬ 
ed an evening star. 

From the greatest elongation of Venus when westward 
of the sun, as at v, to her greatest elongation when east- 


* Many interesting particulars respecting the nature of comets, &c. 
raav be learned by referring to the latter end of the third book of New- 
ton*s Principia. 

t Venus gives the greatest quantity of light to the earth when her 
elongation is 39® 44'. Vince’s Fluxions. 

22 



151 


OF THE PLANETS. 


ward of the sun, as at g, she will appear to go forw ard 
in her orbit, and describe the arc VWHG amongst the 
fixed stars ; bi^t fromg to v she will appear retrograde,^' 
or return to the point V in the heavens in the order GH 
WV. For when Venus is at/, she will be seen amongst 
the fixed stars at H, and when at g she will appear at G: 
when she arrives at h she will again appear at H in the 
heavens. Hence, in a considerable part of her orbit 
b.etween/ and h, and between w and x, she will appear 
nearly in the same point amongst the fixed stars, and at 
these times is said to be stationary. 

When a planet appears to move from the neighbour^ 
hood of any fixed stars, towards others which lie to the 
eastward, jts motion is said to be direct; when it pro¬ 
ceeds towards the stars which lie to the west, its motion 
is retrograde ; and when it seems not to aiter its position 
amongst the fixed stars, it is said to be stationary. 

If the earth stood still at T, the planet Venus would 
seem to make equal vibrations from the sun each way, 
forming the equal angles g TS, and v TS, each 4T° 48'; 
her greatest elongation, and the stationary points w^ould 
alw^ays be in the same place in the heavens ; but it must 
be remembered, that while Venus is proceeding in her 
orbit from a towards a;, the earth is going forward from 
T towards E ; hence, the stationary points and places 
of conjunction and opposition, vary in every revolution. 

What has been observed with respect to Venus, may 
be applied with a little variation to Mercury. 

m. OF THE STATIONARY AND RETROGRADE APPEAR¬ 
ANCES OF THE EXTERIOR PLANETS. 

Because the earth’s orbjt is contained within the orbit 
of Mars, Jupiter, &c. they are seen in all sides of the 
heavens, and are as often in opposition to the sun as iq 
conjunction with him. Let the circle in which T is sit¬ 
uated (Plate IV. Fig. 8.) represent the orbit of the 
earth, and that in which M is situated the orbit of Mars. 
Now, if the earth be at T when Mars is at M, Mars and 


♦ The stationary and retrograde appearances of the inferior planets 
are neatly illustrated by a small orrery, made and sold by Messrs. Wm. 
and S. Jones, Mathematical Instrument-makers, Holborn. 



THE FIXED STARS 


155 


the stin will be in conjunction, but if the earth be at t 
when Mars is at M, they will be in opposition, viz. the 
sun will appear in the east when Mars is in the west. If 
the earth stood still at T, the motion of the planet Mars 
would always appear direct j but the motion of the earth 
being mo;*^ rapid than that of Mars, he will be overtaken 
and passed by the earth. Hence, Mars will have two 
stationary and one retrograde appearance. Suppose 
the earth to be at E when Mars is at M, he will be seen 
in the heavens among the 6xed stars at m ; and for some 
time before the earth has arrived at E, and after it has 
passed E, he will appear nearly in the same point m, 
viz. he will be stationary. While the earth moves 
through the part E t e of its orbit, if Mars stood still at M, 
he would appear to move in a retrograde direction 
through the arc m P r n, in the heavens, and would a- 
gain be stationary at a ; but if, during the time the earth 
moves from E to e. Mars moves from M to O, the arc of 
retrogradation would be nearly m P r. 

The same manner of reasoning may be applied to Ju¬ 
piter and all the superior planets. 

IV. OF THE FIXED STARS. 

The division of the stars into constellations, the marks 
by which they are distinguished. Sec. have already been 
given among the Definitions, from page 23 to 36. 

1. The motion of the fixed stars.—All the fixed stars 
except the polar star, appear to have a diurnal motion 
from east to west; this arises from the diurnal motion of 
the earth on its axis from west to east. The fixed stars 
have also a small apparent motion about their real pla¬ 
ces, arising from the velocity of the earth in its orbit 
combined with the motion of light. This motion is call¬ 
ed the aberration of the fixed stars, and was discovered 
by Dr. Bradley.* They vary in their situations by the 
precession of the equinoxes; hence, their longitudes, &c- 
vary considerably in a series of years, which renders it 
necessary to have new platesf engraven for our celes¬ 
tial globes at least once in about fifty years. 


* The third Astronomer Royal he died in the year 1762. 
t Before the publication of Cary’s Globes and Bardin’s New British 
Globes, there had been no new plates engraven since the time ofSenex. 




156 


THE FIXED STARS. 


Dr. Maskelyne observes* that many, if not all the fix¬ 
ed stars, have small motions among themselves, which 
are called their proper motions ; the cause and laws of 
which, are hid, for the present, in almost equal obscu¬ 
rity. By comparing his observations with others, he 
found the annual proper motion of the following stars, in 
right ascension to be, of Sirius,—0" .63 ; of Castor,— 
0".28; of Procyon,—0".8 ; of Pollux,—0".93 ; of 
Regulus,—0".41 ; of Arcturus,—1".4; of a Aquils 
4-0".5f ; and Sirius increased in north polar distance 
4-1 ".20; Arcturus-f-2".01. 

2. Of the Magnitudes, Distance, Number, and Ap¬ 
pearance of the fixed Stars.—The magnitudes of the 
fixed stars will probably remain for ever unknown ; all 
that we can have reason to expect, is a mere approxima¬ 
tion founded on conjecture. From a comparison of the 
light afforded by a fixed star, and that of the sun, it has 
been concluded that the magnitudes of the stars do not 
differ materially from the sun. The different apparent 
magnitudes of the stars are supposed to arise from their 
different distances ; for the young astronomer must not 
imagine that all the fixed stars are placed in a concave 
hemisphere, as they appear in the heavens, or on a con¬ 
vex surface, as they are represented on a celestial globe. 

From a series of accurate observations by Dr. Brad¬ 
ley on y Draconis, he inferred that its annual parallax 
did not amount to a single second; that is, the diame¬ 
ter of the earth’s annual orbit, which is not less than 190 
millions of miles, would not form an angle at this star of 
one second in magnitude ; or, that it appeared in the 
the same point of the heavens during the earth’s annu¬ 
al course round the sun. 

The same author calculates the distance of y Draco¬ 
nis from the earth to be 400,000 times that of the sun, 
or 38,000,000,000,000 miles : and the distance of the 
nearest fixed star from the earth to be 40,000 times the 
diameter of the earth’s orbit, or 7,600,000,000,000 miles. 
These distances are so immensely great, that it is impos¬ 
sible for the fixed stars to shine by the light of the sun 
reflected from their surfaces : they must therefore, be 
of the same nature with the sun, and like him shine by 
their own light. 


Explanation of the tables, vol. i.of bis Observations. 



THE FIXED STARS. 


157 


The number of the fixed stars is almost infinite, 
though the number which ma^ be seen by the naked 
eye, in the whole heavens does not exceed, and perhaps 
falls short of 3000,* comprehending ail the stars from 
the first to the sixth maguUude inclusive ; but a good 
telescope, directed almost indifferently to any point in the 
heavens, discovers multitudes of stars invisible to the 
naked eye. That bright irregular zone, the milky way, 
has been very carefully examined by Dr. Herschel ; 
who has, in the space of a quarter of an hour, seen 
llfiOOOf stars pass through the field of view of a teles¬ 
cope of only 15' aperture. 

The fixed stars are the only marks by which astrono¬ 
mers are enabled to judge of the course of the moveable 
ones, because they do not vary their relative situations. 
Thus, in contemplating any number of fixed stars, 
which to our view form a triangle, a four-sided figure 
or any other, we shall find that they always retain the 
same relative situation, and that they have had the same 
situation for some thousands of years, viz. from the ear¬ 
liest records of authentic history. But as there are 
few general rules without some exceptions, so this gene¬ 
ral inference is likewise subject to restrictions. Seve¬ 
ral stars, whose situations were formerly marked with 
precision, are no longer to be found ; new ones have al¬ 
so been discovered, which were unknown to the an¬ 
cients ; while numbers seem gradually to vanish, and 
others appear to have a periodical increase and de¬ 
crease of magnitude. Dr. Herschel, in the Philosophi¬ 
cal Transactions for 1783, has given a large collection 
of stars which were formerly seen, but are now lost, to¬ 
gether with a catalogue of variable stars, and of new 
stars. 


* By adding up the numbers of stars in the third column of the Brit¬ 
ish Catalogue given at pages 23, 24, and 25, the sum will be found to 
be 3442. 

t Vince’s Astronomy, or Philosophical Transactions for 1795.—This 
vast multitude of stars, seen and numbered in so short a period of time, 
appears almost incredible, as it would require the doctor to count up¬ 
wards of 128 stars in a second. If the stars were equally disseminated 
through the whole field of view of the telescope, the method of counting 
would be obvious and easy, because the number in the whole could be 
inferred from a small part. 



158 


SOLAR AND LUNAR ECLIPSES- 


The periodical variation of Algol or Persei, is about 
two days 21 hours ; its greatest brightness is of the se¬ 
cond magnitude, and least of the fourth. It varies 
from the second magnitude to the fourth in about 3^- 
hours, and back again in the same time, retaining its 
greatest brightness for the remainder of its period. 

The fixed stars do not appear to be all regularly dis¬ 
seminated through the heavens, but the greater part of 
them are collected into clusters ; and it requires a large 
magnifying power, with a great quantity of light, to dis¬ 
tinguish separately the stars which compose these clus¬ 
ters. With a small magnifying power, and a small quan¬ 
tity of light, they only appear as minute whitish spots, 
like small light clouds, and thence are called nebulae. 
Dr. Herschel has given a catalogue of 2000 nebulae, 
which he has discovered, and is of opinion that the star¬ 
ry heavens are replete with these nebulae. The largest 
nebulae is the milky-way, already noticed at page 34. 

From an attentive examination of the stars with good 
telescopes, many which appear single to the naked eye, 
have been found to consist of two, three, or more stars. 
Dr. Herschel by the help of his improved telescope has 
discovered near 700 such stars. Thus« Herculis, 
^Lyrae, u Geminorum, y Andromeda, a* Herculis, and 
many others, are double stars: v Lyrae, is a triple star ; 
and e Lyrae, ^ Lyrae, a Orionis, and | Libras, are quad¬ 
ruple stars.* 

V. ON SOLAR AND LUNAR ECLIPSES. 

An eclipse of the sun is occasioned by the dark body 
of the moon passing between the earth and the sun, or 
by the shadow of the moon falling on the earth at the 
place where the observer is situated ; hence, all the 
eclipses of the sun happen at the time of the new moon. 
Thus, let S represent the sun (Plate II. Fig, 6.) m the 
moon between the earth and the sun, aEGb a portion of 
the earth’s orbit, e and / two places on the surface of 
the earth. The dark part of the moon’s shadow is 
called the umbra, and the light part, the penumbra ; 


Vince’s Astronomy, chap. xxiv. 




SOLAR AND LUNAR ECLIPSES. 


169 


now it is evident that if a spectator be situated in that 
part of the earth where the umbra falls., that is, between 
e and/, there will be a total eclipse of the sun at that 
place ; at e and/in the penumbra there will be a partial 
eclipse ; and beyond the penumbra there will be no 
eclipse. As the earth is not always at the same dis? 
tance from the moon, if an eclipse should happen when 
the earth is so far from the moon that the lines Fe and 
Cf cross each other before they come to the earth, a 
spectator situated on the earth, in a direct line between 
the centres of the sun and moon, would see a ring of 
light round the dark body of the moon, called an annular 
eclipse ; when this happens their can be no total eclipse 
any where, because the moon’s umbra does not reach 
the earth. People situated in the penumbra will per¬ 
ceive a partial eclipse. 

According to M* de Sejour, an eclipse can never be 
annular longer than 12 min. 24 sec. nor total longer 
than 7 min. 58 sec. The duration of an eclipse of the 
sun can never exceed two hours.* 

As the sun is not deprived of any part of his light 
during a solar eclipse, and the moon’s shadow, in its pas¬ 
sage over the earth from west to east, only covers a 
small part of the earth’s enlightened hemisphere at 
once, it is evident that an eclipse of the sun may be in¬ 
visible to some of the inhabitants of the earth’s enlight¬ 
ened hemisphere, and a partial or total eclipse may be 
seen by others at the same moment of time. 

An eclipse of the moon is caused by her entering the 
earth’s shadow, and consequently, it must happen when 
she is in opposition to the sun, that is at the time of full 
moon, when the earth is between the sun and the mooUf 
Let S represent the sun (Plate If. Fig. 6.) EG the 
earth, and m^the moon in the earth’s umbra, having the 
earth between her and the sun ; DEP and HGP the 
penumbra. Now, the nearer any part of the penumbra 
is to the umbra, the less light it receives from the sun, 
as is evident from the figure ; and, as the moon enters 
the penumbra before she enters the umbra, she gradual¬ 
ly loses her light and appears less brilliant. 


Emerson’s Astronomy, Sect. 7, page S47. 



160 


SOLAR AND LUNAR ECLIPSES. 


The duration of an eclipse of the moon from her first 
touching the earth’s penumbra to her leaving it, cannot 
exceed 5| hours. The moon cannot continue in the 
earth’s umbra longer than 3| hours in any eclipse, neither 
can she be totally eclipsed for a longer period that If 
hour.* As the moon is actually deprived of her light 
during an eclipse, every inhabitant upon the face of the 
earth, who can see the moon, will see the eclipse. 

GENERAL OBSERVATIONS ON ECLIPSES. 

If the orbit of the earth and that of the moon were 
both in the same plane, there would be an eclipse of the 
sun at every new moon, and an eclipse of the moon at 
every full moon. But the orbit of the moon makes an 
angle of about 5f degrees with the plane of the orbit of 
the earth, and crosses it in two points called the nodes; 
inow astronomers have calculated that, if the moon be 
less than 17° 21' from either node, at the time of new 
moon, the sun may be eclipsed ; or if less than 11° 34' 
from either node, at the full moon, the moon may be 
eclipsed ; at all other times there can be no eclipse, for 
the shadow of the moon will fall either above or below 
the earth at the time of new moon : and the shadow of 
the earth will fall either above or below the moon at the 
time of full moon. To illustrate this, suppose the right 
hand part of the moon’s orbit (Plate II. Fig. 6.) to be 
elevated above the plane of the paper, or earth’s orbit, 
it is evident that the earth’s shadow, at full moon, would 
fall below the moon ; the left hand part of the moon’s 
orbit at the same time would be depressed below the 
plane of the paper, and the shadow of the moon, at the 
time of new moon, would fall below the earth. In this 
case, the moon’s nodes would be between E and a, and 
between G and h, and there would be no eclipse, either 
at the full or new moon ; but, if the part of the moon’s 
orbit between G and b be elevated above the plane of 
the paper, or earth’s orbit; the part between E and a 
will be depressed, the line of the moon’s nodes will then 


^ Emerson’s Astronomy. Sect. T. page S39. 



SOLAR AND LUNAR ECLIPSES. 


161 


pass through the centre of the earth and that of the 
moon, and an eclipse will ensue.* An eclipse of the 
sun begins on the western side of his disc, and ends on 
the eastern; and an eclipse of the moon begins on the 
eastern side of her disc, and ends on the western. 

NUMBER OF ECLIPSES IN A YEAR. 

The average number of eclipses in a year is four, two 
of the sun, and two of the moon; and, as the sun and 
moon are as loilg below the horizon of any particular 
place as they are above it, the average number ot visible 
eclipses in a year is two, one of the sun, and one of the 
moon ; the lunar eclipse frec[ueiltly happens a fortnight 
after the solar one, or the solar one a fortnight after the 
lunar one. 

The most general number of eclipses, in any year, is 
four; there are sometimes six eclipses in a year, but 
there cannot be more than seven, nor fewer than two<» 

The reason will appear, by considering that the sun 
cannot pass both the nodes of the moon’s orbit moro 
than once a year, making four eclipses, except he pass 
one of them in the beginning of the year ; in this case 
he may pass the same node again a little before the end 
of the year, because he is about 173f days in passing 
from one node to the other ; therefore, he may return to 
the same node in about 346 days, which is less than a 
year, making six eclipses. As twelve lunations,J or 
354 days from the eclipse in the beginning of the year, 
may produce a new moon before the year is ended, 
which, (on account of the retrograde motion of the 


* If you draw the figure on card paper, and cut out the moon, her 
shadow and orbit, so as to turn on the line a E G 6, &c. the above illus* 
tration will be rendered more familiar. 

t rhe moon's nodes have a retrograde motion of about 19|. degrees 
in a year (see page 133;) therefore the sun will have to move (180®-— 
191 

ITOi degrees from one node to the other. But it has been 

shown in a preceding note (see page 13.) that the sun's apparent ^diur¬ 
nal moiion is about. 59' in a day ; hence, 59': 1 day :: 170|.« ; lT3days. 

J That is, limes Si9 days 12 hours 44 min. 3 sec, or 354 days 8 
hours 48 min. 36 sec. 


23 



162 


SOLAR AND LUNAR ECLIPSES. 


moon’s nodes) may fall within the solar limit, it is possi¬ 
ble for seven eclipses to4iappen in a year, five of the 
sun and two of the moon. When the moon changes in 
either node, she cannot be near enough to the other 
node at the time of the next full moon to'be eclipsed, 
and in six lunar months afterwards, or about 177 days, 
she will change near the other node ; in this case there 
cannot be more than two eclipses in a year, and both of 
the sun. 

The ecliptic limits of the sun are greater than those 
of the moon, and hence, there will be more solar than 
lunar eclipses, in the ratio of 17^ 21' to 11® 34', or near¬ 
ly of 3 to 2 ; but more lunar than solar eclipses are 
seen at any given place, because a lunar eclipse is visi¬ 
ble to a whole hemisphere at once ; whereas, a solar e- 
clipse is visible only to a part, as has been observed be¬ 
fore, and therefore, there is a greater probability of see¬ 
ing a lunar than a solar eclipse. 


PART III. 


CONTAINING, 


Problems performed by the Terrestrial and Celestial Globes. 


CHAPTER I. 


Problems •performed by the Terrestrial Globe, 


PROBLEM I. 


To find the Latitude of any given Place, 

RULE. Bring the given place to that part of the 
brass meridian which is numbered from the equator to¬ 
wards the poles; the degree above the place is the lati¬ 
tude. If the place be on the north side of the equator, 
the latitude is north ; if it be on the south side the lati¬ 
tude is south. 

On small globes the latitude of a place cannot be found nearer than 
to about a quarter of a degree Each degree of the brass meridian on 
the largest globes is generally divided into three equal parts, each part 
containing twenty geographical miles ; on such globes the latitude may 
be found to 10'. 

Examples. 1. What is the latitude of Edinburgh ? 

Answer. 56® North. 

2. Required the latitude of the following places : 

Amsterdam Florence Philadelphia 


Archangel Gibralter 

Barcelona Hamburgh 

Batavia Ispahan 

Bencoolen Lausanne 

Berlin Lisbon 

Cadiz Madras 

Canton Madrid 

Dantzic Naples 

Drontheim Paris 


Quebec 

Rio Janeiro 

Stockholm 

Turin 

Vienna 

Warsaw 

Washington 


Wilna 

York 


164 


PROBLEMS PERFORMED BY 


3. Find all the places on the globe which have no 
latitude. 

4. What is the greatest latitude a place can have ? 

PROBLEM 11. 

7’o find all those places which have the same Latitude 
as any given place* 

Rule. Bring the given place to that part of the brass 
meridian which is numbered from the equator towards 
the poles, and observe its latitude ; turn the globe round, 
and all places passing under the observed latitude are 
those required. 

All places in the same latitude have the same length of day and night 
and the same seasons of the year, though, from local circumstances, they 
may not have the same atmospherical temperature. See the note, 
page 15. 

Examples. 1. What places have the same, or nearly 
the same latitude as Madrid ? 

Answer. Minorca, Naples, Constantinople, Samarcand, Philadel¬ 
phia, Sec. 

2. What inhabitants of the earth have the same length 
of days as the inhabitants of Edinburgh ? 

3. What places have nearly the same latitude as Lon¬ 
don ? 

4. What inhabitants of the earth have the same sea¬ 
sons of the year as those of Ispahan ? 

5. Find all the places of the earth which have the 
longest day the same length as at Port Royal in Ja- 
piaicao 

PROBLEM III. 

To find the Longitude of any place. 

Rule. Bring the given place to the brass meridian, 
the number of degrees on the equator, reckoning from 
the meridian passing through London to the brass meri¬ 
dian, is the longitude. If the place lie to tjie right hand 
of the meridian passing through London, the longitude 
is east; if to the left hand, the longitude is west. 

On Adams’ globes there are two rows of figures above the equator. 
When the place lies on the right hand of the meridian of London, the 
longitude must be counted on the upper line ; when it lies to the left 
hand, it must be counted on the lower line. Bardin’s New British 
Globes have also two rows of figures above the equator, but the lower 
Hne is always used in reckoning the longitude. 


THE TERRESTRIAL GLOBE. 165 


Examples* 1. What is the longitude of Petersburg ? 

Answer. east. 

2. What is the longitude of Philadelphia? 

Answer. 75:^® west. 


3. Required the longitude of the following places : 


Aberdeen 
Alexandria 
Barbadoes 
Bombay 
Botany Bay 
Canton 
Carlscrona 
Cayenne 


Civita Vecchia 
Constantinople 
Copenhagen 
Drontheim 
Ephesus 
Gibralter 
Leghorn 
Liverpool 


Lisbon 
Madras 
Masulipatum 
Mecca 
Nankin 
Palermo 
Pondicherry 
Queda 


4. What is the greatest longitude a place can have ? 


PROBLEM IV. 


To find all those places that have the same Longitude 
as a given place* 

Rule* Bring the given place to the brass meridian, 
then all places under the same edge of the meridian 
from pole to pole have the same longitude. 

All people situated under the same meridian from 66» 28' north lati¬ 
tude to 66® £8' south latitude, have noon at the same time : or, if it be 
one, two, three, or any number of hours before or after noon with one 
particular place, it will be the same hour with every other place situa¬ 
ted under the same meridian 

Examples* 1. What places have the same, or nearly 
the same longitude as Stockholm ? 

Answer. Dantzic, Presburg, Tarento, the Cape of Good Hope, &c. 

2. What places have the same longitude as Alexan¬ 
dria ? 

3. When it is ten o’clock in the evening at London, 
what inhabitants of the earth have the same hour ? 

4. What inhabitants of the earth have midnight when 
the inhabitants of Jamaica have midnight ? 

5. What places of the earth have the same longitude 
as the following places ? 

London Quebec The Sandwich islands 

Pekin Dublin Pelew islands 


166 


PROBLEMS PERFORMED BY 


PROBLEM V. 

To find the Latitude and Longitude of any place. 

Rule. Bring fhe given place to that part of the brass 
meridian, which is numbered from the equator towards 
fhe poles ; the degree above the place is the latitude, and 
the degree on the equator, cut by the brass meridian, 
is the longitude. 

This problem is only an exercise of the first and third. 

Examples. 1. What are the latitude and longitude of 
Petersburg ? 

Answer. Latitude 60° N. longitude E. 

2. Required the latitudes and longitudes of the fol¬ 
lowing places : 


Acapulco 

Cusco 

Leith 

Aleppo 

Copenhagen 

Lizard 

Algiers 

Durazzo 

Lubec 

Archangel 

Elsinore 

Malacca 

Belfast 

Flushing 

Manilla 

Bergen 

Cape Guardafui 

Medina 

Buenos Ayres 

Hamburgh 

Mexico 

Calcutta 

Jeddo 

Mocha 

Candy 

Jaffa 

Moscow 

Corinth 

Ivica 

Oporto 


PROBLEM VI. 


To find anyplace on the globe, having the latitude and 
longitude of that place given. 

Rule, Find the longitude of the given place on the 
equator, and bring it to that part of the brass meridian 
which is numbered from the equator towards the poles ; 
then under the given latitude, on the brass meridian, you 
will find the place required. 

Examples, 1. What place has 151^° east longitude, 
and 34° south latitude. 

Answrer. Botany Bay. 

2. What places have the following latitudes and lon^ 
gitudes ? 


THE TERRESTRIAL GLOBE. 


167 


Latitudes. 

Longitudes. 

Latitudes. Longitudes. 

50° 

6' N. 

5° 

54' W. 

19° 

26'N. 100° 6'W. 

48 

12 N. 

16 

16 £. 

59 

56 N. 30 19 E. 

55 

58 N. 

3 

12 W. 

0 

13 s. rr 55 w. 

52 

22 N. 

4 

51 E. 

46 

55 N. 69 53 W. 

81 

13 N. 

29 

55 E. 

59 

21 N. 18 4 E. 

64 

34 N. 

38 

58 E. 

8 

32 N. 81 11 E. 

34 

29 S. 

18 

23 E. 

5 

9 S. 119 49 E. 

3 

49 S. 

102 

10 E. 

22 

54 S. 42 44 W. 

34 

35 S. 

58 

31 W. 

36 

5 N. 5 22 W. 

32 

25 N. 

52 

50 E. 

32 

38 N. ir 6 W. 


PROBLEM VII. 


To find the difference of Latitude between any two 
places. 

Rule. Bring one of these places to that half of the 
brass meridian which is numbered from the equator to¬ 
wards the poles, and mark the degree above it; then 
bring the other place to the meridian, and the number 
of degrees between it and the above mark will be the 
difference of latitude. 

Or, find the latitudes of both the places (by Prob. I.) 
Then, if the latitudes be both north or both south, sub¬ 
tract the less latitude from the greater, and the remain¬ 
der will be the difference of latitude : but, if the latitudes 
be one north and the other south, add them together, and 
their sum will be the difference of latitude. 

Examples. 1. What is the difference of latitude be¬ 
tween Philadelphia and Petersburg ? 

Answer. 20 degrees. 

2. What is the difference of latitude between Madrid 
and Buenos Ayres ? 

Answer. 75 degrees. 

3. Required the difference of latitude between the 
following places ? 


London and Rome 
Delhi and Cape Comorin 
Vera Cruz and Cape Horn 
Mexico and Botany Bay 
Astracan and Bombay 
St. Helena and Manilla 
Copenhagen and Toulon 
Brest and Inverness 
Cadiz and Sierra Leone 


Alexandria and the Cape of 
Good Hope 
Pekin and Lima 
St. Salvador and Surinam 
Washington and Quebec 
Porto Bello and the Straits 
of Magellan 

Trinidad Land Trincomalc 
Bencoolen and Calcutta 




16B PROBLEMS PERFORMED BY 

4. What two places on the globe have the greatest 
difference of latitude ? 

PROBLEM VIII. 


To find the difference of Longitude between any two 
places. 


Rule. Bring one of the given places to the brass me¬ 
ridian, and mark its longitude on the equator ; then bring 
the other places to the brass meridian, and the number of 
degrees between its longitude and the above mark, 
counted on the equator, the nearest way round the 
globe, will show the difference of longitude. 

Or, find the longitudes of both the places (by Prob. 
III.) then, if the longitudes be both east or both west, 
subtract the less longitude from the greater, and the re¬ 
mainder will be the difference of longitude ; but, if the 
longitudes be one east and the other west, add them to¬ 
gether, and their sum will be the difference of longi¬ 
tude. 

When this sum exceeds 180 degrees, take it from 
360, and the remainder will be the difference of longi¬ 
tude. 

Examples. 1. What is the difference of longitude 
between Barbadoes and Cape Verd ? 

Answer. 41* 48' 


2. What is the difference of longitude between Buenos 
Ayres and the Cape of Good Hope ? 

Answer. 76* 50'. 

3. What is the difference of longitude between Bota- 
ny Bay and OVhy’ee ? 

Answer. 52* 45', or 52|*. 


4. Required the difference of longitude between the 
following places 


Vera Cruz and Canton 
Bergen and Bombay 
Cohimbo and Mexico 
Juan Fernandes I. and Ma¬ 
nilla 

Pelew I. and Ispahan 
Boston in Amer. and Berlin 


Constantinople and Batavia 
Bermudas I. and I.of Rhodes 
Port Patrick and Berne 
Mount Heckla and Mount 
Vesuvius 

Mount .^tna and Teneriffe 
North Cape and Gibralter 


5. What is the greatest difference of longitude com¬ 
prehended between two places ? 



THE TERRESTRIAL GLOBE. 


169 


PROBLEM IX. 

To find the d istance between any two places. 

Rule. The shortest distance between any two pk- 
ces on the earth, is an arc of a great circle contained 
between the two places. Therefore, lay the graduated 
edge of the quadrant of altitude over the two places, so 
that the division marked O may be one of the places, 
the degrees on the quadrant comprehended between the 
two places will give their distance ; and if these degrees 
be multiplied by 60^ the product will give the distance 
in geographical miles; or multiply the degrees by 69^, 
and the product will give the distance in English miles. 

Or, take the distance between the two places with a 
pair of compasses, and apply that distance to the equa¬ 
tor, which will show how many degrees it contains. 

If the distance between the two places should exceed 
the length of the quadrant, stretch a piece of thread over 
the two places, and mark their distance ; the extent of 
thread between these marks, applied to the equator, from 
the meridian of London, will show the number of de¬ 
grees between the two places. 

Examples 1. What is the nearest distance between 
the Lizard and the island of Bermudas f 


45S distance in degrees. 
60 

2700 

30 

15 

2745 geographical miles. 


45| distance in degrees. 
69i 

221 

405 

270* 

341 

in 


31791 English miles. 

2. What is the nearest distance between the island of 
l^ermndas and Bt. Helena ? 


24 




170 


PROBLEMS PERFORMED BY 


73i distance in degrees. 
60 


4380 

30 


4410 geographical miles. 


73i distance in degrees. 
69L 


363 
657 
438 • 

5108} English miles. 

London and 

154 distance in degrees. 
691 


77 

1386 

924 


10703 English miles. 


3. What ia the nearest distance between 
Botany Bay ? 

154 distance in degrees. 

60 


9240 geograpliical miles. 


4. What is the direct distance between London and 
Jamaica, in geographical and in English miles T 

5. What is the extent of Europe in English miles from 
Cape Matapan in the Morea, to the North Cape in 
Lapland ? 

6. What is the extent of Africa from Cape Verd to 
Cape Guardafui ? 

7. What is the extent of South America from Cape 
Blanco in the West to Cape St. Roque in the east ? 

8. Suppose the track of a ship to Madras be from the 
Lizard to St. Anthony, one of the Cape Verd Islands, 
thence to St. Helena, thence to the Cape of Good Hope, 
thence to the east of the Mauritius, thence a little to the 
south-east of Ceylon, and thence to Madras; how many 
English miles is the Land’s End from Madras ? 

Simple as the preceding problem may appear in theory, on a superfi¬ 
cial view, yet, when applied to practice, the difficulties which occur are 
almost insuperable. In sailing across the trackless ocean, or travelling 
through extensive and unknown countries, our only guide is the com¬ 
pass, and except two places be situated directly north and south of each 
other, or upon the equator, though we may travel or sail from one place 
to the other by the compass, yet we cannot take the shortest route, as 
measured by the quadrant of altitude. 












the terrestrial globe. 


171 


To illustrate these observations by examples ; first, Let two places 
be situated in latitude 50° north, and differing in longitude 48° 50', 
which will nearly correspond with the Land's End and the eastern coast 
of Newfoundland. The arc of nearest distance being that of a great 
circle, truly calculated by spherical trigonometry, is ^° 49' 6", eo^ual 
to 1849_i_ geographical miles, or 214t| English miles; but, if a ship 

steer from the Land's End directly westward in the latitude of 50° north» 
till her difference of longitude be 48° 50', her true distance sailed will be 
188S|. geographical miles, or 2i81^ English miles, making a circuitous 

course of S4_3_ geographical miles, or 40S English miles Those who 

are acquainted with spherical trigonometry and the principles of navi¬ 
gation, particularly great cirde sailing, know that it is impossible to 
conduct a ship exactly on the arc of a great circle, except, as before 
observed, on the equator or a meridian : for, in this example, she must 
be steered through all the different angles, from N. 70° W, to 

90 degrees, and continue sailing from thence through all the same va¬ 
rieties of angles, till she arrives at the intended place, where the angle 
will become 70° 49' 30", the same as at first. 

Secondly. Suppose it were required to find the shortest distance be¬ 
tween the Lizard, lat. 49° 57' N. long. 5° 21' W. and the island of Ber¬ 
mudas, lat. 32° 35' N. long. 63° 32' W. The arc of a great circle con¬ 
tained between the two places, will be found, by spherical trigonome¬ 
try to be 45° 44', being 2744 geographical miles, or 3178 English miles. 
See the method of calculating such problems in Keith’s Trigonometry, 
second edition, page 278. Now, for a ship to run this shortest track, 
she must sail from the Lizard 89° 29' W. and gradually lessen her 
course so as to arrive at Bermudas on the rhumb bearing S. 49° 47' W. 
but this, though true in theory, is impracticable: the course and distance 
must therefore be calculated by Mercator's sailing. The direct course 
by the compass will be found to be S. 68° 9' W., and the distance upon 
that course 2800 geographical miles, or 3243 English miles ; making a 
circuitous course of 56 geographical miles, or 65 English miles. 

Hence, to find the distance between any two places whose latitudes and 
longitudes are known^ in order to travel or sail from any place to the o- 
ther, on a direct course by the mariner^s comjmss, the following methods 
must be used. ' 

1. If the places be situated on the same meridian, their difference of 
latitude w^ill be the nearest distance between them in degrees, and the 
places will be exactly north and south of each other. 

2. If the places be situated on the equator, their difference of longitude 
will be the nearest distance in degrees, and the places will be exactly 
east and west of each other. 

3. If the places differ both in latitudes and longitudes, the distance 
between them and the point of the compass on which a person roust sail 
or travel, from the one place to the other, must be found by Merca¬ 
tor’s Sailing, as in navigation. 

4. If the pieces be situated in the same latitude, they will be direct¬ 
ly east and west of each other; and their difference of longitude, multi¬ 
plied by the number of miles which make a degree in the given lati¬ 
tude, according to the following table, will give the distance. 


172 


PROBLEMS PERFORMED BY 


Deg. 

Lat, 

Geog. 

Miles. 

English 

Miles. 

Lat. 

Deg. 

Geog. 

Miles. 

English 

Miles. 

3eg. 

Eat. 

. Geog. 
Miles. 

English 

Miles. 

0 

60.00 

69.07 

31 

51 . 43 ' 

59.13 

61 

29.09 

33.45 

1 

59.99 

69.06 

32 

50.88 

58.51 

62 

28.17 

32.40' 

2 

59.96 

69.03 

33 

50.32 

57.87 

63 

27.24 

31.33 

3 

59.92 

68.97 

34 

49.74 

57.20 

64 

26.30 

30.24 

4 

59.85 

68.90 

35 

49.15 

56-51 

65 

25.36 

29.15 

5 

59.77 

68.81 

36 

48.54 

55.81 

66 

24.40 

28.06 

6 

59.67 

68.62 

37 

47.92 

55.10 

67 

23.45 

26.96 

7 

59.55 

68-48 

38 

47.28 

54.37 

68 

22.48 

25-85 

8 

59.42 

68.31 

39 

46 63 

53.62 

69 

21.50 

24.73 

9 

59.26 

68.15 

40 

45.96 

52.85 

70 

20.52 

23.60 

10 

59.09 

67.95 

41 

45.28 

5207 

71 

19.53 

22.47 

11 

58.89 

67.73 

42 

44.59 

51.27 

72 

18.54 

21.32 

12 

58.69 

67.48 

43 

43.88 

50.46 

73 

17.54 

20.17 

13 

58.46 

67.21 

44 

43.16 

49.63 

74 

16.54 

19.02 

U 

58.22 

66.95 

45 

42.43 

48.78 

75 

15.53 

17.86 

15 

57.95 

66.65 

46 

41.68 

47.93 

76 

14.52 

16.70 

16 

57.67 

66.31 

47 

40.92 

47.06 

77 

13.50 

15 52 

17 

57.38 

65.98 

48 

40.15 

46.16 

78 

12.48 

14.35 

18 

57.06 

65.62 

49 

39.36 

45.26 

79 

11.45 

13-17 

19 

56.73 

65.24 

50 

38.57 

44-35 

80 

10.42 

il.98 

20 

56.38 

64.84 

51 

37 76 

43 42 

81 

9.38 

10.79 

21 

56.01 

64.i2 

52 

36.94 

42.48 

82 

8.35 

9 59 

22 

55.63 

63.97 

53 

3641 

41 53 

83 

7.31 

8.41 

23 

55.23 

6351 

54 

35.27 

40.56 

84 

6.27 

7.21 

24 

54.81 

63.03 

55 

34.41 

39.58 

85 

5.22 

6.00 

25 

54.38 

62.53 

56 

33.53 

38.58 

86 

4.18 

4-81 

26 

53.93 

62.02 

57 

32.68 

37.58 

87 

3.14 

3.61 

27 

5346 

6148 

58 

31.79 

36 57 

38 

2.09 

2.41 

28 

52.97 

60.93 

59 

30.90 

35.54 

89 

1.05 

1.21 

29 

52.48 

60.35 

60 

30.00 

34.50 

90 

0.00 

0.00 

30 

51.96 

59.75 

Length of a degree 69.07 English miles. 


^ The foregoing taWe is calculated thus; radius is to the length of a 
degree upon the equator, as the co-sine of the given latitude is to the 
length of a degree in that latitude. See this proportion illustrated m 
Keith’s Trigonometry, page 261, second edition. 


























THE TERRESTRIAL GLOBE, 


173 


PROBLEM X. 

A ‘place being given on the globe, to find all places 

which are situated at the same distance from it as 

any other given place. 

Rule. Lay the graduated edge of the quadrant of 
altitude over the two places, so that the division mark¬ 
ed O may be on one of the places, then observe \rhat de¬ 
gree of the quadrant stands over the other place; move 
the quadrant entirely round, keeping the division mark¬ 
ed O in its first situation, and £ill places which pass un¬ 
der the same degree which was observed to stand over 
the other place, will be those sought. 

Or, place one foot of a pair of compasses in one of the 
given places, and extend the other loot to the other giv¬ 
en place ; a circle described from the first place as a 
centre, with this extent, will pass through all the places 
sought. 

If the distance between the two given places should exceed the 
length of the quadrant, or the extent of a pair of compasses, stretch 
a piece of thread over the two places, as in the preceding prob¬ 
lem. 

Examples. 1. It is required to find all the places on 
the globe wich are situated at the same distance from. 
London as Warsaw is ? 

Answer. Koningsburg, Buda, Posega, Alicant, &c. 

2. What places are at the same distance from Lon¬ 
don as Petersburg is ? 

3. What places are at the same distance from Lon¬ 
don as Constantinople is ? 

4. What places are at the same distance from Rome 
as Madrid is ? 


PROBLEM XL 

Given the latitude of a place and Us distance from a 
given place, to find that place whereof the latitude is 
given. 

Rule, If the distance be given in English or geogra¬ 
phical miles, turn them into degrees, by dividing by 69| 
for English miles, or 60 for geographical miles ; then 


174 


PROBLEMS PERFORMED BY 


put that part of the graduated edge of the quadrant of 
altitude which is marked O upon the given place, and 
move the other end eastward or westward (according 
as the required place lies to the east or west of the giv¬ 
en place) till the degrees of distance cut the given par¬ 
allel of latitude ; under the point of intersection you 
will hnd the place sought. 

Or, Having reduced the miles into degrees, take the 
same number of degrees from the equator with a pair of 
compasses, and with one foot of the compass in the 
given place, as a centre, and this extent of degrees, de¬ 
scribe a circle on the globe ; turn the globe till this cir¬ 
cle falls under the given latitude on the brass meridian, 
and you will find the place required. 

Examples, I. A place in latitude 60® N. is 1320J 
English miles from London, and it is situated in E. lon¬ 
gitude ; required the place ? 

Answer. Divide 1320^ miles by 69^ miles, or, which is the same 
thing, 2641 half miles by 139 half miles, the quotient will give 19 de¬ 
grees; hence, the required place is Petersburg. 

2. A place in latitude 32^® N. is 1350 geographical 
miles from London, and it is situated in W. longitude ; 
required the place ? 

Answer. Divide t3r>0 by 60, the quotient is22® 30', or22J degrees; 
hence, the required place is the west point of the island of Madeira. 

3. What place, in E. longitude and 41® N. latitude, 
is 1529 English miles from London? 

4. What place, in W. longitude and 13® N. latitude 
is 3660 geographical miles from London ? 

PROBLEM XII. 

Given the longitude of a place and its distance from a 

given placcj to find that place whereof the longitude^ 

is given. 

Rule, If the distance be given in English or geo¬ 
graphical miles, turn them into degrees by dividing by 
69| for English miles, or 60 for geographical miles; 
then, put that part of the graduated edge of the quad¬ 
rant of altitude which is marked O upon the given place, 
and move the other end northward or southward (accor¬ 
ding as the required place lies to the north or south of 


THE TERRESTRIAL GLOBE. 175 

the given place,) till the degrees of distance cut the 
given longitude ; under the point of intersection you 
will find the place sought. 

Or, Having reduced the miles into degrees, take the 
game number of degrees from the equator with a pair of 
compasses, and with one foot of the compasses in the 
given place, as a centre, and this extent of degrees, de¬ 
scribe a circle on the globe ; bring the given longitude 
to the brass meridian, and you will find the place, upon 
the circle, under the brass meridian. 

Examples. 1. A place in north latitude, and in 60 
degrees west longitude, is 4239^ English miles from 
London ; required the place ? 

Answer. Divide 4239^ miles by 69^ miles, or, which is the same 
thing, 8479 half miles by 139 half miles, the quotient will give 61 de¬ 
grees ; hence, the required place is the island of Barbadoes. 

2. A place in north latitude, and in 75^ degrees west 
longitude, is 3120 geographical miles from London ; 
what place is it ? 

3. A place in 31i degrees east longitude, and situa¬ 
ted southward of London, is 2224 English Miles from it; 
required the place ? 

4. A place in 29 degrees east longitude, and situated 
southward of London, is 1529 English miles from it; 
required the place ? 


PROBLEM XIU. 

To find how many miles make a degree of longitude 
in any given parallel of latitude. 

Rule. Lay the quadrant of altitude parallel to the 
equator between any two meridians in the given latitude, 
which differ in longitude 15 degrees ;* the number of 
degrees intercepted between them multiplied by 4, will 
give the length of a degree in geographical miles. The 
geographical miles may be brought into English miles, 
by multiplying by 116, and cutting off two figures from 
the right hand of the product. 


* The meridiaDS on Cary’s large globes are drawn through every ten 
degrees. The rule will answer for these globes, by reading 10 degrees 
for 15 degrees, and multiplying by 6 instead of 4. 



176 


PROBLEMS PERFORMED BY 


Or, Take the distance between two meridians, which 
differ in longitude 15 degrees in the given parallel of 
latitude, with a pair of compasses ; apply this distance 
to the equator, and observe how many degrees it makes ; 
with wliich proceed as above. 


Since the quadrant of altitude will measure no arc truly but that of' 
a great circle ; and a pair of compasses will only measure the chord of 
an arc, not the arc itself; it follows, that the preceding rule cannot be 
mathematically true, though sufficiently correct for practical purposes. 
When great exactness is required, recourse must be had to calculation. 
See the table in the note to Problem IX, page 170. 

The above rule is founded on a supposition that the number of de¬ 
grees contained between any two meridians, reckoned on the equator, 
is to the number of degrees contained between the same meridians, on 
any parallel of latitude, as the number of geographical miles contained 
in one degree of the equator, is to the number of geographical miles con¬ 
tained in one degree on the given parallel of latitude. Thus in the 
latitude of London, two places which differ 15 degrees in longitude are 
degrees distant by the rule. Hence, 15® ; 9^® : : 60 m. : 37 ra. or 
15® : 60 m. ; : 9^® : 37 ra. but 15 is to 60 as 1 is to 4, therefore, 1 : 4 
: : 9^ t 37 geographical miles contained in one degree. Now, any 
number of geographical miles may be brought into English miles by 
multiplying by 69^ and dividing by 60; or by multiplying by 1.16, 
for 60 : 69^ : : 1 : 1-16 nearly. * 

Examples. 1. How many geographical and English 
miles make a degree in the latitude of Pekin ? 

Answer. The latitude of Pekin is 40® north : the distance between 
two meridians in that latitude (which differ in longitude 15 degrees) is 
1degrees. Now, 11^ degrees multiplied by 4, produces 46 geograph¬ 
ical miles for the length of a degree of longitude, in the latitude of Pe¬ 
kin ; and if 46 be multiplied hyii.6, the product will be 5336 ; cut off 
the two right hand figures, and the length of a degree in English miles 
will be 53. Or, by the rule of three 15® : 69^ m. ; : 11|® : 53 miles. 


2. How many miles make a degree in the parallels of 
latitude wherein the following places are situated ? 


Surinam 
Barbadoes 
Havannah 
Bermudas I. 


Washington 
Quebec 
Skalholt 
North Cape 


Spitzbejrgen 
Cape Verd 
Alexandria 
Paris 


PROBLEM XIV. 


To find the bearing of one place from another. 

Rule. If both the places be situated in the same 
parallel of latitude, their bearing is either east or west 
from each other ; if they be situated on the same merid¬ 
ian, they bear north and south from each other ; if they 


THE TERRESTRIAL GLOBE. 


177 


be situated on the same rhumb-line,* that rhumb-line is 
their bearing; if they be not situated on the same rhumb¬ 
line, lay the quadrant of altitude over the two piaces, 
and that rhumb-line which is the nearest of being paral¬ 
lel to the quadrant will be their bearing. 

Or, if the globe have no rhumb-lines drawn on it, 
make a small mariner’s compass (such as in Plate I, 
Fig. 4.) and apply the centre of it to any given place, 
80 that the north and south points may coincide with 
some meridian ; the other points will show the bearing 
of all the circumjacent places, to the distance of up¬ 
wards of a thousand miles, if the centrical place be nbt 
far distant from the equator. 

Examples, 1. Which way must a ship steer from 
the Lizard to the island of Bermudas ? 

Answer .W.S.W. 

2. Which way must a ship steer from the Lizard to 
the island of Madeira ? 


Answer. S.S.W. 

3. Required the bearing between London and the foh 
lowing places : 

Amsterdam Copenhagen Petersburg 
Athens Dublin Prague 

Bergen Edinburgh Rome 

Berlin Lisbon Stockholm 

Berne Madrid Vienna 

Brussels Naples Warsaw 

Buda Paris 


PROBLEM XV. 


To find the angle of position between two places. 

Rule, Elevate the north or south pole, according as 
the latitude is north or south, so many degrees above 
the horizon as are equal to the latitude of one of the giv- 


* On Adams’ globes there are two compasses drawn on the equator, 
each point of which may be called a rhumb-line, being drawn so as to 
cut all the meridians in equal angles. One compass is drawn on a va¬ 
cant place in the Pacific ocean, between America and New Holland; 
and another, in a similar manner, in the Atlantic, between Africa, and 
South America. There are no Rhumb-lines, on either Cary’s or 
Bardin’s globes. 


25 



178 


PROBLEMS PERFORMED BY 


cn places ; bring that place to the brass meridian, and 
screw the quadrant of altitude upon the degree over it; 
next move the quadrant till its graduated edge falls upon 
the other place; then the number of degrees on the wood¬ 
en horizon, between the graduated edge of the quadrant 
and the brass meridian, reckoning towards the elevated 
pole, is the angle of position between the two places. 

Examples. 1. What is the angle of position between 
London and Prague ? 

Answer. 9() degrees from the north, towards the east; the quadrant 
of altitude will fall upon the east point of the horizon, and pass over or 
near the following places, viz. Rotterdam, Frankfort, Cracow, Ock- 
zakow, Calfa, south part of the Caspian Sea, Guzerat in India, Mad¬ 
ras, and part of the island of Ceylon. Hence, all these places have the 
same angle of position from London. 

2. What is the angle of position between London and 
Port Royal in Jamaica ? 

Answer. 90 degrees from the north towards the west; the quadrant 
of altitude will fail upon the west point of the horizon. 

3. What is the angle of position between Philadelphia 
and Madrid ? 


Answer. 65 degrees from the north towards the east; the quadrant 
of altitude will fall between the E.N.E. and N.E. by E. points of the 
horizon. 


4. Required the angles of position between London 
and the following places ? 

Amsterdam Copenhagen Rome 

Berlin Cairo Stockholm 

Berne Lisbon Petersburg 

Constantinople Madras Quebec 


The preceding problem has been the occasion of many disputes 
among writers on the globes. Some suppose the angle of position to 
represent the true bearing of two pla¬ 
ces, viz. that point of the compass upon 
which any person must constantly sail or 
travel, from the one place to the other ; 
while others contend, that the angle of 
position between two places is very dif¬ 
ferent from their bearing by the mari¬ 
ner’s compass. We shall here endea¬ 
vour to set the matter in a clear point 
of view. The annexed figure represents 
a quarter of the sphere, stereographi- 
cally projected on the plane of the meri¬ 
dian, with the half meridians and paral¬ 
lels of latitude drawn through every ten 
degrees ; P represents the north pole, and E€t a portion of the equa¬ 
tor. JNow, by attending to the manner of finding the angle of nosi- 
tiOD, as laid down in the foregoing problem, we shall find that the quad- 







THE TERRESTRIAL GLOBE. 


17;9 

rant of altitude always forms the base of a spherical triangle, the two 
sides of which triangle are the compliments of the latitudes of the two 
places, and the vertical angle is their difference of longitude. Phe 
angles at the base of this triangle are the angles of position between 
the two places. 

1 . When the two places are situated on the samepaf-^ 
allel of latitude. 

Let two places L and O be situated in latitude 50 north, and differ¬ 
ing in longitude 48° 50', which will nearly correspond with the Land’s 
End and the eastern coast of Newfoundland (See the note to Prob. IX.) 
then OP and LP will be each 40 degrees, the angle OPL, measured by 
the arc will be 48° 50' ; whence the arc of nearest distance O 71 L 
may be found (by case III. page 225, Keith’s Trigonometry) being 
30° 39'6", the angle PLO equal to POL, the triangle being isosceles, 
is TO® 49' SO" ; and if n be the middle point between L and O, the lati¬ 
tude of that point will be found to be 52° 3T' north, and the angles 
PnL and PnO will be right angles. Now, if an indefinite number of 
points be taken along the edge of the quadrant of latitude, viz. on the 
arc LnO, the angle of position between L and each of these points will 
be N. 70° 49' SO" W.; but, if it wer«g possible for a ship to sail along 
the arc LnO by thejcompass, her latitude would gradually increase be¬ 
tween L and n, from 50° N. to 52° 37' N ; and the courses she must 
steer would vary from 70° 49' SO" at L. to 90° atn. In sailing from 
n to O, she must decrease her latitude from 52° 37' N. to 50° N and 
her courses must var/ from 90°, or directly west, to 70° 49' SO"; but, if 
a ship were to sail along the parallel of latitude LmO, her course would 
be invariably due west. Hence, it follows that, if two places be situa¬ 
ted on the same parallel of latitude, the angle of position between 
them cannot represent their true bearing by the mariner’s compass. 

CoRoLiiA-RV. If the two places were situated on the equator as at 
w and Q,, the angle of position between Gt and w, and between Q, and 
all the intermediate points as at N, would be 90 degrees. In this case 
therefore, and in this only, the angle of position shows the true bearing 
by the compass. 

3 . If the two places differ both in latitudes and Ion- 

gitudes. 


Let L represent a place in latitude 50° N ; B a place in latitude 
13° SO' N. and let their difference of longitude BPL, measured by thq 
arc hOi be 52° 58'. The angle of position between L and B (calcula¬ 
ted by spherical trigonometry) will be found to be S. 68° 57' W. and 
the angle of position between B and L will be N..38° 5'E. whereas, 
the direct course by the compass from L to B (calculated by Mercator’s 
Sailing) is S. 50° 6' W. and from B to L, it is N. 50° 6' E. If we as¬ 
sume any number of points on the arc LB, the angle of position be¬ 
tween L and each of these points will be invariable, viz. PLr, PL<, 
PLy, PLa, PLr, &c. are each equal to 68° 57': while the angle of po¬ 
sition between each of these places and L, viz. PuL, P<L, PyL, PaL, 
PrL, &c. are continually diminishing. If a ship, therefore, were to 
^il from L, on a S. 68° 57' W. course by the mariner’s compass, she 


180 


PKOBUiMS PERFORMED BY 


would never arrive at B; and were she to sail from B, on a N. 38° 6' E. 
course by the compass, she would never arrive at L. 

Hence, an angle of position between two places cannot represent 
their bearing, except those places be on the equator, or upon the same 
meridian. 

PROBLEM XVI. 

To find the Antceci, PericBci, and Antipodes of 
any place. 

Rule. Place the two poles of the globe in the horizon, 
and bring the given place to the eastern part of the hori¬ 
zon; then, if the given place be in north latitude, ob¬ 
serve how many degrees it is to the northward of the 
east point of the horizon ; the same number of degrees 
to the southward of the east point will show the Antoeci; 
an equal number of degrees, counted from the west 
point of the horizon towards the north, will show the 
Perioeci; and the same number of degrees, counted to¬ 
wards the south or west, will point out the Antipodes. 
If the place be in south latitude the same rule will se«ve 
by reading south fer north, and the contrary. 

OR THUS ; 

For the Antceci. Bring the given place to the brass 
meridian and observe its latitude, then in the opposite 
hemisphere, under the same degree of latitude, you will 
find the Antocci. 

For the Periceci. Bring the given place to the brass 
meridian, and set the index of the hour circle to 12, turn 
the globe half round, or till the index points to the other 
12, then under the latitude of the given place you will 
find the Perioeci. 

For the Antipodes. Bring the given place to the 
brass meridian, and set the index of the hour circle to 
12, turn the globe half round, or till the index points to 
the other 12, then under the same degree of latitude 
with the given place, but in the opposite hemisphere, 
you will find the Antipodes. 

Examples. 1. Required the Antceci, Perioeci, and 
Antipodes of the island of Bermudas. 

Answer. A place in Paraguay, a little N. W. of Buenos Ayres, is 
the Antceci; Periceci is a place in China N. W. of Nankin; and the 
S.W.part of New Holland is the Antipodes. 


the terrestrial globe. 181 

2. Required the Antoeci, Perioeci, and Antipodes of 
the Cape of Good Hope. 

3. Captain Cook, in one of his voyages, was in 50 de¬ 
grees south latitude and 180 degrees of longitude; in 
what part of Europe were his Antipodes ? 

4. Required the x\ntcEci of the Falkland Islands. 

5. Required the Perioeci of the Philippine Islands. 

6. What inhabitants of the earth are Antipodes to 
Buenos Ayres ? 


PROBLEM XVIL 

To find at what rate per hour the inhabitants of any 
given place are carried, from west to east, by the rev¬ 
olution of the earth on its axis. 

Ride. Find how many miles make a degree of longi¬ 
tude in the latitude of the given place (by Problem 
XIII.) which multiply by 15 for the answer. 

Or, look for the latitude of the given place in the ta¬ 
ble, Problem IX, against which you will find the num¬ 
ber of miles contained in one degree, multiply these by 
15, and reject two figures from the right hand ofthepror 
duct; the result will be the answer. 

Examples, 1. At what rate per hour are the inhabi¬ 
tants of Madrid carried from west to east by the revo¬ 
lution of the earth on its axis. 

Answer. The latitude of Madrid is about 40* N. where a degree of 
longitude measures 46 geographical or 53 English miles (see Ex¬ 
ample 1. Prob. XIII.) Now, 46 multiplied by 15 produces 690, and 
53 multiplied by 15 produces 795 ; hence, the inhabitants of Madrid are 
carried 690 geographical or 795 English miles per hour. 

By the Table. Against the latitude of 40 you will find 45.96 geo¬ 
graphical miles, and 52.85 English miles : Hence, 

45.96 X15 = 689.40 and 52.85 X 15=792.75, by rejecting the two 
right hand figures from each product, the result will be 689 geographical 
miles, and 792 English miles, agreeing nearly with the above. 

2. At what rate per hour are the |inhabitant3 of the 
following places carried from west to east by the revo¬ 
lution of the earth on its axis ? 


* The reason of this rule is obvious, for if m be the number of miles 
contained in a degree, we have 24 hours; 360® X m.:: 1 hour: the an¬ 
swer ; but, 24 is contained 15 times in 360; therefore, 1 hour; 15 X m * * 
1 hour: the answer. that is, on a supposition that the earth turns on 
its axis from west to east in 24 hours; but we have before observed that 
it turns on its axis in 23 hours 56 min. 4 sec., which will make a small 
diSerence not worth notice. 



PROBLEMS PERFORMED BY 


U2 


Skalbolt 

Spilzbergen 

Petersburg 

London 


Philadelphia Cape of Good Hope 

Cairo Calcutta 

Barbadoes Delhi 

Quito Batavia 


PROBLEM XVIII. 


particular place and the hour of the day at that place 
being given^ to find what hour it is at any other 
place* 

Rule* Bring the place at which the time is given to 
the brass meridian, and set the index of the hour circle 
io 12 turn the globe till the other place comes to the 
meridian, and the hours passed over by the index will 
be the difference of time between the two places. If the 
place where the hour is sought lie to the east of that 
wherin the time is given, count the difference of time 
forward from (he given hour; if it lie to the west, reckon 
the difference of time backward. 


OR, WITHOUT THE HOUR CIRCLE. 

Find the difference oflongitude between the two pla¬ 
ces (by Problem VIII.) and turn it into time by allow¬ 
ing 15 degrees to an hour, or four minutes of time to one 
degree. The difference of longitude in lime, will be 
the difference of time between the two places, with 
which proceed as above. Degrees oflongitude may be 
turned into time by multiplying by 4 ; observing that 
minutes or miles oflongitude, when multiplied by 4, pro¬ 
duce seconds of time, and degrees of longitude, when 
multiplied by 4, produce minutes of time. 

It has been remarked in the note page 5, that some globes have two 
rows of figures on the hour circle, others but one ; this difference fre¬ 
quently occasions confusion ; and the manner in which authors in gene¬ 
ral direct a learner to solve those problems wherein the hour circle is 
used, serves only to increase that confusion. In this, and in all the 
succeeding problems, great care has been taken to render the rules gene¬ 
ral for any hour circle whatsoever. 

Examples* 1. When it is ten o’clock in the morning 
at London, what hour is it at Petersburg ? 


* The index may be set to any hour, but 12 is the most convenient 
io count from, and it is immaterial which 12 on the hour circle tho m- 
dex is set to, 



THE TERRESTRIAL GLOBE. 


183 


Answer. The difference of time is two hours; and, as Petersburg is 
eastward of London, this difference mast be counted forward, so that it 
is twelve o’clock at noon at Petersburg. 

Or, the difference of longitude between Petersburg and London is 
SQo ^ 5 / which multiplied by 4 produces 2 hours 1 rain. 40 sec. the differ¬ 
ence of time shown by the clocks of London and Petersburg; heiicc, as 
Petersburg lies to the east of London, when it is ten o’clock in the 
morning at London, it is one minute and forty seconds past twelve at 
Petersburg. 

2. When it is twelve o^clock in the afternoon at Alex¬ 
andria in Egypt, what hour is it at Philadelphia ? 

Answer. The difference of time is seven hours; and because Phila¬ 
delphia lies to the west of Alexandria, this difference must be reckoned 
backward, so that it is seven o’clock in the morning at Philadelphia. 

Or, The longitude of Alexandria is SO® 16' E. 

The longitude of Philadelphia is 75 19 W. 


Difference of longitude 105 35 

4 


Difference of longitude in time 7 h. 2 m. 20 sec., the 
alocks at Philadelphia are slower than those at Alexandria; hence, 
when it is two o’clock in the afternoon at Alexandria, it is 57 m. 40 
sec. past six in the morning at Philadelphia. 

3. When it is noon at London, what hour is it at Cal¬ 
cutta ? 

4. When it is ten o’clock in the morning at London, 
what hour is it at Washington ? 

5. When it is nine o’clock in the morning at Jamai¬ 
ca, what o’clock is it at Madras T 

6. My watch was well regulated at London, and when 
I arrived at Madras, which was after a five month’s 
voyage, it was four hours and fifty minutes slower than 
the clocks there. Had it gained or lost during the voy¬ 
age ? And how much ? 


PROBLEM XIX. 


A particular place and the hour of the day being given 
to find all places on the globe where it is then noon^ 
or any other given hour. 

Rule, Bring the given place to the brass meridian, 
and set the index of the hour circle to 12; then, as the 
difference of time between the given and required pla¬ 
ces is always known by the problem, if the hour at the 
required places be earlier than the hour at the given 
place, turn the globe eastward till the index has passed 
over as many hours as are equal to the given difference 




184 


PROBLEMS PERFORMED BY 


of time ; but, if the hour at the required places be later 
than the hour at the given place, turn the globe west¬ 
ward till the index has passed over as many hours as are 
equal to the given difference of time; and in each case, 
all the places required will be found under the brass 
meridian. 


OR, WITHOUT THE HOUR CIRCLE. 

Reduce the difference of time between the given 
place and the required places into minutes ; these min¬ 
utes, divided by 4, will give degrees of longitude; if there 
be a remainder after dividing by 4, multiply it by 60, 
and divide the product by four, the quotient will be min¬ 
utes or miles of longitude. The difference of longitude 
between the given place and the required places being 
thus determined, if the hour at the required places be 
earlier than the hour at the given place, the required 
places lie so many degrees to the westward of the given 
place as are equal to the difference of longitude; if the 
hour at the required places be later than the hour at the 
given place, the required places lie so many degrees to 
the eastward of the given place as are equal to the dif¬ 
ference of longitude. 

Examples, 1. When it is noon at London, at what 
place is it ^ past eight o’clock in the morning ? 

Answer. The difference of time between London, the given place, 
and the required places, is hours, and the time at the required places 
is earlier than that at London ; therefore, the required places lie 3^ 
hours westward of London; consequently, by bringing to London the 
brass meridian, setting the index to 12, and turning the globe eastward 
till the index has passed over 3^ hours, all the required places will be 
under the brass meridian, as the eastern coast of Newfoundland, Cay¬ 
enne, part of Paraguay, &c. 

Or, the difference of time between London, the given place, and the 
required places, is 3 hours SO min. 

3 h. SO m. The difference of longitude between the 

60 given place and the required places is 52® SO'. 

■■■ — . - The hour at the required places being earlier 

4)210 m. than that at the given place, they lie 52® SO' 

—- westward of the given place. Hence, all pla- 

52 o — 2 ces situated in 52° 30' west longitude from 

60 London are the places sought, and will be 

-- found to be Cayenne, See, as above. 

4)120 


SOm- 




the terrestrial globe. 


185 


2. When it is two o’clock in the afternoon at London, 
at what place is it | past five in the afternoon ? 

Answer. Here the difference of time between London, the given place, 
and the requited places, is 3^ hours; but the time at the required pla^ 
ces is later than at London. The operation will be the same as in ex* 
ample 1, only the globe must be turned hours towards the west, be¬ 
cause the required places will be in east longitude, or eastward of the 
given place. The places sought are the Caspian sea, western part of 
Nova Zembla, the island of Socotra, eastern part of Madagascar, &c. 

3. When it is | past four in the afternoon at Paris, 
where is it noon ? 

4. When it is | past seven in the morning at Ispahan, 
where is it noon f 

5. When it is noon at Madras, where is it ^ past six 
o’clock in the morning ? 

6. At sea in latitude 40° north, when it was ten o’¬ 
clock in the morning by the time piece, which shows the 
hour at London, it was exactly 9 o’clock in the morn¬ 
ing at the ship, by a correct celestial observation. In 
what part of the ocean was the ship ? 

7. When it is noon at London, what inhabitants of the 
earth have midnight ? 

8. When it is 10 o’clock in the morning at London^ 
where is it ten o’clock in the evening ? 

PROBLEM XX. 

To find thesun^s longitude (commonly called the sun^s. 

place in the eclijytic) and his declination* 

Rule. Look for the given day in the circle of months 
on the horizon, against which, in the circle of signs, are 
the sign and degree in which the sun is for that day. 
Find the same sign and degree in the ecliptic on the sur¬ 
face of the globe ; bring the degree of the ecliptic, thus 
found, to that part of the brass meridian which is num¬ 
bered from the equator towards the poles, its distance 
from the equator reckoned on the brass meridian, is the 
sun’s declination.—This problem may be performed by 
the celestial globe, using the same rule. 


26 


186 


PKOliLEiMS PERFORMED BY 


OR BY THE ANALEMMA.* 


Bring the analemma to that part of the brass meridian 
which is numbered from the equator towards the poles, 
and the degree on the brass meridian, exactly above the 
day of the month, is the sun’s declination. Turn the 
globe till a point of the ecliptic, correspondent to the 
day of the month, passes under the degree of the sun’s 
declination, that point will be the sun’s longitude or 
place for the given day. If the sun’s declination be 
north, and increasing, the sun’s longitude will be some¬ 
where between Aries and Cancer. If the declination 
be decreasing, the longitude will be between Cancer and 
Libra. If the sun’s declination be south, and increas¬ 
ing, the sun’s longitude will be between Libra and Cap¬ 
ricorn ; if the declination be decreasing, the longitude 
will be between Capricorn and Aries. 

The sun’s longitude and declination are given in the second page of 
every month, in the Nautical Almanac, for every day in that month ; 
they are likewise given in White’s Ephemeris, for every day in the year. 

Examples, 1. What is the sun’s longitude and de¬ 
clination on the 15th of April ? 

Answer. The sun’s place is 26° in ^, declination 10° N. 

2. Required the sun’s place and declination for the 
following days : 


January 21. 
February 7. 
March 16. 
April 8. 


May 18. 
June 11. 
July 11. 
August 1. 


September 9. 
October 16. 
November 17, 
December 1. 


* The analemma is properly an orthographic projection of the 
sphere on the plane of the meridian; but what is called the analemma 
on the globe, is a narrow slip of paper, the length of which is equal to 
the breadth of the torrid zone. It is pasted on some vacant place on 
the globe in the torrid zone, and is divided into months, and days of the 
months, correspondent to the sun’s declination for every day in the 
year. It is divided into two parts; the right hand part begins at the 
winter solstice, or December 21st, and is reckoned upwards towards 
the summer solstice, or June 21st, where the left hand part begins, 
which is reckoned downwards in a similar manner, or towards the win¬ 
ter solstice. On Cary’s globes the Analemma somewhat resembles the 
figures. It appears to have been drawn in this shape for the conven¬ 
ience of showing the equation of time, by means of a straight line 
which passes through the middle of it. The equation of time is placed 
on the horizon of Bardin’s globes. 






THE TERRESTRIAL GLOBE. 
PROBLEM XXL 


1«7 


To place the globe in the same silnation with respect to 
the suuy as our earth is at the EqiiinoxeSy at the sum¬ 
mer solstice, and at the winter solstice, and thereby to 
show the comparative lengthsof the longest and short¬ 
est days.^ 

1. For the equinoxes. Place Ihe two poles of tbe 
globe in the horizon ; for at this time the sun has no de¬ 
clination, being in the equinoctial in the heavens, which 
is an imaginary line standing vertically over (he equa¬ 
tor on the earth. Now, if we suppose the sun to be fix¬ 
ed ; at a considerable distance from (he globe, vertical¬ 
ly over that point of the brass meridian which is marked 
O, it is evident that the wooden horizon will be the 
boundary of light and darkness on the globe, and (hat (he 
upper hemisphere will be enlightened from pole to pole. 

Meridians, or lines of longitude, being generally drawn 
on the globe through every 15 degrees of the equator, 
the sun will apparently pass from one meridian to ano¬ 
ther in an hour. If you bring the point Aries on the e- 
quator to the eastern part of the horizon, the point Libra 
will be in the western part thereof : and (he sun will 
appear to be setting to the inhabitan(s of London and 
to all places under the same meridian ; let the globe be 
now turned gently on its axis towards (he east, the sun 
will appear to move towards the west, and, as (he dif¬ 
ferent places successively en(er the dark hemisphere, 
the sun will appear to be selling in (he west. Continue 
the motion of the globe eastward, till London comes to 
the western edge of the horizon; the moment it emerges 
above the horizon, the sun will appear to be rising in the 
east. If the motion of the globe on i(s axis be contin¬ 
ued eastward, the sun will appear to rise higher and 
higher, and to move towards the west; when London 


* In this problem, as in all others where the pole is elevated to the 
sun’s declination, the sun is supposed to be fixed, and the earth to move 
on its axis from west to east. The author of this work has a little brass 
ball made to represent the sun ; this ball is fixed upon a telescope. The 
socket is made to screw upon the brass meridian (of any globe) over the 
sun’s declination, and the little brass ball, representing the sun, stands 
over the declination, at a considerable distance from the globe. 



18a 


PROBLEMS PERFORMED BY 


comes fo the brass meridian, the sun will appear at its 
greatest height; and after London has passed the brass 
meridian, he will continue his apparent motion westward, 
and gradually diminish in altitude till London comes to 
the eastern part of the horizon, when he will again be 
setting. During this revolution of the earth on its axis, 
every place on its surface has been twelve hours in the 
dark hemisphere, and twelve hours in the enlightened 
hemisphere; consequently, the days and nights are equal 
all over the world ; for all the parallels ot latitude are 
divided into two equal parts by the horizon, and in eve¬ 
ry'degree of latitude there are six meridians between 
the eastern part of the horizon and the brass meridian ; 
each of these meridians answers to one hour, hence, half 
the length of the day is six hours, and the whole length 
twelve hours. 

If an}^ place be brought to the brass meridian, the 
number of degrees between that place and the horizon 
(reckoned the nearest way) will be the sun’s meridian 
altitude. Thus, if London be brought to the meridian, 
the sun will then appear exactly south, and its altitude 
will be 381 degrees; the sun’s meridian altitude at Phi¬ 
ladelphia will be 50 degrees ; his meridian altitude at 
Quito 90 degrees ; and here, as in every place on the 
equator, as the globe turns on its axis, the sun will be 
vertical. At the Cape of Good Hope the sun will ap¬ 
pear due north at noon, and his altitude will be 65^ de- 
grees. 

2. For the Summer Solstice —The summer solstice, to 
the inhabitants of north latitude, happens on the 21st of 
June, when the sun enters Cancer, at which time his de¬ 
clination is 23° 28' north. Elevate the north pole 23^ 
degrees above the northern point of the horizon, bring 
the sign of Cancer in the ecliptic to the brass meridian, 
and over that degree of the brass meridian under which 
this sign stands, let the sun be supposed to be fixed at a 
considerable distance from the globe. 

While the globe remains in this position, it will be 
seen that the equator is exactly divided into two equal 
parts, the equinoctial point Aries being in the western 
part of the horizon, and the opposite point Libra in the 
eastern part, and between the horizon and the brass me¬ 
ridian (counting on the equator) ther^ are six meridians;^ 


THE TERRESTRIAL GLOBE. 


189 


each fifteen degrees, or an hour apart, consequently, the 
day at the equator is twelve hours long. From the e- 
quator northward, as far as the Arctic circle, the diurnal 
arcs will exceed the nocturnal arcs; that is, more than 
one half of any of the parallels of latitude will be above 
the horizon, and of course less than one half will be be¬ 
low, so that the days are longer than the nights. All 
the parallels of latitude within the Arctic circle will be 
wholly above the horizon, consequently, those inhabitants 
will have no night. From the equator southward, as 
far as the Antarctic circle, the nocturnal arcs will exceed 
the diurnal arcs : that is, more than one half of any one 
of the parallels of latitude will be below the horizon, 
and consequently less than one half will be above. All 
the parallels of latitude within the Antarctic circle will 
be wholly below the horizon, and the inhabitants, if any, 
will have twilight or dark night. 

From a little attention to the parallels of latitude while 
the globe remains in this position, it will easily be seen 
that the arcs of those parallels which are above the ho¬ 
rizon, north of the equator, are exactly of the same length 
as those below the horizon, south of the equator; conse¬ 
quently, when the inhabitants of north latitude have the 
longest day, those in south latitude have the longest 
night. It will likewise appear, that the arcs of those 
parallels which are above the horizon, south of the e- 
quator, are exactly of the same length as those below 
(he horizon north of the equator ; therefore, when the 
inhabitants who are situated south of the equator have 
the shortest days, those who live north of the equator 
have the shortest nights. 

By counting the number of meridians (supposing them 
to be drawn through every fifteen degrees of the equa¬ 
tor) between the horizon and the brass meridian on any 
parallel of latitude, half the length of the day will be de¬ 
termined in that latitude, the double of which is the 
length of the day. 

1. In the parallel of 20 degrees north latitude, there 
are six meridians and two thirds more, hence, the long¬ 
est day is 13 hours and 20 minutes ; and, in the parallel 
of 20 degrees south latitude, there are five meridians and 
one third, hence, the shortest day in that latitude is ten 
Ijours and forty minuteso 


190 


PROBLEMS PERFORMED BY 


2. In the parallel of 30 degrees north latitude, there 
are seven meridians between the horizon and (he brass 
meridian, hence, the longest day is 14 hours; and in 
the same degree of south latitude, there are only five 
meridians, hence, the shortest day in that latitude is ten 
hours. 

3. In the parallel of 50 degrees north latitude there 
are eight meridians between the horizon and the brass 
meridian ; the longest day is therefore sixteen hours ; 
and in the same degree of south latitude there are on¬ 
ly four meridians; hence, the shortest day is eight 
hours. 

4. In the parallel of 60 degrees north latitude, there 
are meridians from the horizon to the brass meridian, 
hence, the longest day is hours ; and, in the same de¬ 
gree of south latitude there are only 2|^ meridians, the 
length of the shortest day is therefore 5^ hours. 

By turning the globe gently round on its axis from 
west to east we shall readily perceive that the sun will 
be vertical to all the inhabitants under the tropic of Can¬ 
cer as the places successively pass the brass meridian. 

If any place be brought to the brass meridian, the 
number of degrees between that place and the horizon 
(reckoned the nearest way) will show the sun’s meridian 
altitude. Thus, at London, the sun’s meridian altitude 
will be found to be about 62 degrees ; at Petersburg 
54ji degrees, at Madrid 73 degrees, &.c. To the inhabi¬ 
tants of these places the sun appears due south at noon. 
At Madras the sun’s meridian altitude will be 79J de¬ 
grees, at the Cape of Good Hope 32 degrees, at Cape 
Horn 10| degrees, &c. The sun will appear due north 
to the inhabitants of these places at noon. If the south¬ 
ern extremity of Spitzbergen, in latitude 76| north, be 
brought to that part of the brass meridian, which is num¬ 
bered from the equator towards the poles, the sun’s 
meridian altitude will be 37 degrees, which is its great¬ 
est altitude ; and if the globe be turned eastward twelve 
hours, or till Spitzbergen comes to that part of the brass 
meridian which is numbered from the pole towards the 
equator, the sun’s altitude will be 10 degrees, which is 
its least altitude for the day given in the problem. It 
was shown, in the foregoing part of the problem, that, 
when the sun is vertical over the equator in the vernal 


THE TERRESTRIAL GLOBE. 


191 


equinox, the north pole begins to be enlightened, conse¬ 
quently, the farther the sun apparently proceeds in his 
course northward, the more day-light will be diffused 
over the north polar regions, and the sun will appear 
gradually to increase in altitude at the north pole, till the 
21st of June, when his greatest height is 23| degrees ; 
he will then gradually diminish in height till the 23d of 
September, the time of the autumnal equinox, when he 
will leave the north pole and proceed towards the south; 
consequently, the sun has been visible at^the north pole 
for six months. 

3. For the Winter Solstice-.l^he winter solstice, to the 
inhabitants of north latitude, happens on the 21st of De¬ 
cember, when the sun enters Capricorn, at which time 
his declination is 23° 28' south. Elevate the south pole 
23| degrees above the southern point of the horizon, 
bring the sign of Capricorn in the ecliptic to the brass 
meridian, and over that degree of the brass meridian un¬ 
der which the sign stands, let the sun be supposed to be 
fixed at a considerable distance from the globe. 

Here, as at the summer solstice, the days at the equa¬ 
tor will be 12 hours long, but the equinoctial point 
Aries will be in the eastern part of the horizon, and Libra 
in the western. From the equator southward, as far as 
the Antarctic circle, the diurnal arcs will exceed the 
nocturnal arcs. All the parallels of latitude within the 
Antarctic circle will be wholly above the horizon. From 
the equator northward, the nocturnal arcs will exceed 
the diurnal arcs. All the parallels of latitude within 
the Arctic circle will be wholly below the horizon. The 
inhabitants south of the equator will now have their 
longest day, while those on the north of the equator will 
have their shortest day. 

As the globe turns on its axis from west to east, the 
sun will be vertical successively to all the inhabitants 
under the tropic of Capricorn. By bringing any place 
to the brass meridian, and finding the sun’s meridian ah 
titude (as in the foregoing part of the problem,) the 
greatest altitudes will be in south latitude, and the least 
in the north ; contrary to what they were before. Thus, 
at London, the sun’s greatest altitude will be only 15 
degrees, instead of 62; and his greatest altitude at Cape 
Horn will now be 57^ degrees, instead of 10|, as at the 


192 


PROBLEMS PERFORMED BY 


summer solstice; hence, it appears, that the ditference 
between the sun’s greatest and least meridian altitude at 
any place in the temperate zone, is equal to the 
breadth of the torrid zone, viz. 47 degrees, or more cor¬ 
rectly 46° 56'. On the 23d of September, when the 
sun enters Libra, that is, at the time of the autumnal e- 
quinox, the south pole begins to be enlightened, and, as 
the sun’s declination increases southward, he will shine 
farther over the south pole, and gradually increase in al¬ 
titude at the pole ; for, at all times, his altitude at either 
pole is equal to his declination. On the 21st of Decem¬ 
ber the sun will have the greatest south declination, after 
which his altitude at the south pole will gradually di¬ 
minish as his declination diminishes ; and on the 21st of 
March, when the sun’s declination is nothing, he will ap¬ 
pear to skim along the horizon at the south pole, and 
likewise at the north pole ; the sun has therefore been 
visible at the south pole for six months. 

PROBLEM XXII. 

To place the globe in the same siluation, with respect 
lo the Polar Star in the heavens, as our earth is to 
the inhabitants of the equator, Ike. vis. to illustrate 
the three positions of the sphere, Right Parallel, and 
Oblique, so as to show the comparative length of the 
longest and shortest days,^ 

1. For the Right Sphere .—The inhabitants who 
live upon the equator have a right sphere, and the north 
polar star appears always in (or very near) the horizon. 
Place the two poles of the globe in the horizon, then 
the north pole will correspond with the north polar star, 
and all the heavenly bodies will appear to revolve round 
the earth from east to west, in circles parallel to the 
equinoctial, according to their different declinations : 


♦ In this problem, and in all others where the pole is elevated to 
the latitude of a given place, the earth is supposed to be fixed, and the 
sun to move round it from east to west. When the given place is 
brought to the brass meridian, the wooden horizon is the true rational 
horizon of that place, but it does not separate the enlightened part of 
the globe from the dark part, as in the preceding problem. 



THE TERRESTRIAL GLOBE. 


193 


one half of the starry heavens will be constanlly above 
the horizon, and the other half below, so that the stars 
will be visible for twelve hours, and invisible for the 
same space of time ;and, in the course of a year, an in¬ 
habitant upon the equator may see all the stars in the 
heavens. The ecliptic being drawn on the terrestrial 
globe, young students are often led to imagine that the 
sun apparently moves daily round the earth in the same 
oblique manner. To correct this false idea, we must 
supjjpse the ecliptic to be transferred to the heavens, 
where it properly points out the sun’s apparent annual 
path amongst the fixed stars. The sun’s diurnal path 
is either over the equator, as at the time of the equinox¬ 
es, or in lines nearly parallel to the equator: this may 
be correctly illustrated by fastening one end of a piece 
of packthread upon the point Aries on the equator, and 
winding the packthread round the globe towards the 
right hand, so that one fold may touch another, till you 
come to the tropic of Cancer ; thus you will have a cor¬ 
rect view of the sun’s apparent diurnal path from (he 
vernal equinox to the summer solstice ; for, after a diur¬ 
nal revolution the sun does not come to the same point 
of the parallel whence it departed, but, according 
as it approaches to, or recedes from the tropic, is a little 
above or below that point. When the sun is in the 
equinoctial, he will be vertical to all the inhabitants upon 
the equator, and his apparent diurnal path will be over 
that line ; when the sun has ten degrees of north decli¬ 
nation, his apparent diurnal path will be from east to 
west nearly along that parallel. When the sun has ar¬ 
rived at the tropic of Cancer, his diurnal path in the 
heavens will be along that line, and he will be vertical to 
all the inhabitants on the earth in latitude 23*^ 28' north. 
The inhabitants upon the equator will always have 
12 hours day and twelve hours night, notwithstanding 
the variation of the sun’s declination from north to south, 
or from south to north; because the parallel of latitude 
which the sun apparently describes for any day will al¬ 
ways be cut into two equal parts by the horizon. The 
greatest meridian altitude of the sun will be 90°, and the 
least 66® 32'. During one half of the year, an inhabi¬ 
tant on the equator will see the sun full north at noon, 
and during the other half it will be full south. 


194 


PROBLEMS PERFORMED BY 


2. For the Parallel Sphere. —The inhabitants (if 
any) who live at the north pole have a parallel sphere, 
and the north polar star in the heavens appears exactly 
(or very nearly) over their heads. Elevate the north 
pole ninety degrees above the horizon, then the equator 
will coincide with the horizon, and all the parallels of 
latitude will be parallel thereto. In the summer half 
year, that is from the vernal to the autumnal equinox, 
the sun will appear above the horizon, consequently, 
the stars and planets will be invisible during that jperi- 
od. When the sun enters Aries, on the 2l8tof March, 
he will be seen by the inhabitants of the north pole (if 
there be any inhabitants) to skim just along the 
edge of the horizon ; and, as he increases in declination, 
he will increase in altitude, forming a kind of spiral as 
before described, by wrapping a thread round the globe. 
The sun’s altitude at any particular hour is always 
equal to his declination. The greatest altitude the sun 
can have is 23” 28', at which time he has arrived at 
the tropic of Cancer ; after which he will gradually de¬ 
crease in altitude as his declination decreases. When 
the sun arrives at the sign Libra, he will again appear 
to skim along the edge of the horizon, after which he 
will totally disappear, having been above the horizon 
for six months. Though the inhabitants at the north 
pole will lose sight of the sun a short time after the au¬ 
tumnal equinox, yet the twilight will continue for nearly 
two months; for the sun will not be 18° below the ho¬ 
rizon till he enters the 20th of Scorpio, as may be seen 
by the globe. 

After the sun has descended 18° below the horizon, 
all the stars in the northern hemisphere will become 
visible, and appear to have a diurnal revolution round 
the earth from east to west, as the sun appeared to have 
when he was above the horizon. These stars will not set 
during the winter half of the year; and the planets, when 
they are in any of the northern signs, will be visible. 
The inhabitants under the north polar star have the 
moon constantly above their horizon during fourteen 
revolutions of the earth on its axis, and at every full 
moon which happens from the 23d of September to the 
21st of March, the moon is in some of the northern signs, 
and consequently, visible at the north pole ; for the 
sun being below the horizon 8t that time, the moon must 


the terrestrial globe. 


195 


be above Ihe horizon, because she is always in that sign 
which is diametrically opposite to Ihe sun at the time of 
full moon. 

When the sun is at his greatest depression below the 
horizon, being then in Capricorn, the moon is at her 
first quarter in Aries : full in Cancer: and at her third 
quarter in Libra : and as the beginning of Aries is the 
risingpoint of the ecliptic. Cancer the highest, and Libra 
the setting point, the moon rises at her first quarter in 
Aries, is most elevated above the horizon and full in 
Cancer, and sets at the beginning of Libra in her third 
quarter ; having been visible for fourteen revolutions of 
the earth on its axis, viz. during the moon’s passage 
from Aries to Libra. Thus the north pole is supplied 
one half of the winter time with constant moonlight in 
the sun’s absence ; and the inhabitants only lose sight 
of the moon from her third to her first quarter, while 
she gives but little light, and can be of little or no ser¬ 
vice to them. 

3. For the Oblique Sphere. —Whenever the terres¬ 
trial globe is placed in a proper situation with respect 
to the fixed stars, the pole must be elevated as many 
degrees above the horizon as are equal to the latitude 
of the given place, and the north pole of the globe must 
point to the north polar star in the heavens ; for in sail¬ 
ing, or travelling from the equator northward, the north 
polar star appears to rise higher and higher. On the equa¬ 
tor it will appear in the horizon; in ten degrees of north 
latitude it will be ten degrees above the horizon ; in twen¬ 
ty degrees of north latitude it will be twenty degrees a- 
bove the horizon ; and so on, always increasing in altitude 
as the latitude increases. Every inhabitant of the earth, 
except those who live upon the equator, or exactly un¬ 
der the north polar star, has an oblique sphere, viz. the 
equator cuts the horizon obliquely. By elevating and 
depressing the poles, in several problems, a young stu¬ 
dent is sometimes led to imagine that the earth’s axis 
moves northward and southward just as the pole is rais¬ 
ed or depressed : this is a mistake, the earth’s axis has 
no such motion.* In travelling from the equator north- 


* The earth^s axis has a kind of librating motion, called the nuta¬ 
tion, but this cannot be represented by elevating or depressing the 
pole. 



1% 


PROBLEMS PERFORMED BV 


ward, our horizon varies; thus, when we are on the 
equator, the northern point of our horizon is exactly op¬ 
posite the north polar star ; when we have travelled to 
ten degrees north latitude, the north point of our horizon 
is ten degrees below the pole, and so on : now, the wood¬ 
en horizon on the terrestrial globe is immovable, other¬ 
wise it ought to be elevated or depressed, and not the 
pole ; but whether we elevate the pole ten degrees 
above the horizon, or depress the north point of the 
horizon ten degrees below the pole, the appearance will 
be exactly the same. 

The latitude of London is about 51^ degrees north : 
if London be brought to the brass meridian, and the 
north pole be elevated 51^ degrees above the north 
point of the wooden horizon, then the wooden horizon 
will be the true horizon of London ; and, if the artificial 
globe be placed exactly north and south by a mariner’s 
compass, or by a meridian line, it will have exactly the 
position which the real globe has. JNow, if we imagine 
lines to be drawn through every degree* within the 
torrid zone, parallel to the equator, they will nearly 
represent the sun’s diurnal path on any given day. 
By comparing these diurnal paths with each other, they 
will be found to increase in length from the equator 
northward, and to decrease in length from the equator 
southward ; consequently, when the sun is north of the 
equator, the days are increasing in length ; and when 
south of the equator, the days are decreasing. The 
sun’s meridian altitude for any day may be found by 
counting the number of degrees from the parallel in 
which the sun is on that day, towards the horizon, upon 
the brass meridian ; thus, when the sun is in that paral¬ 
lel of latitude which is ten degrees north of the equator, 
his meridian altitude will be 48L degrees. Though the 
wooden horizon be the true horizon of the given place, 
yet it does not separate the enlightened hemisphere of 
the globe from the dark hemisphere, when the pole is 
thus elevated. For instance, when the sun is in Aries, 
and London at the meridian, all the places on the globe 
above the horizon, beyond those meridians which pass 


Such lines are drawn on Adams’ globes. 




the terrestrial globe. 


197 


through the east and west points thereof, reckoning 
towards the north, are in darkness, notwithstanding they 
are above the horizon ; and all places below the hori¬ 
zon, between those same meridians and the southern 
point of the horizon, have day-light notwithstanding they 
are below the horizon of London. 

PROBLEM XXIII. 

The month and day of the month being given, to find 
all places of the earth where the sun is vertical on 
that day ; those places where the sun does not set, 
and those places where he does not rise on the given 
day. 

Rule. Find the sun’s declination (by ProblemXX.) 
for the given day, and mark it on the brass meridian ; 
turn the globe round on its axis from west to east, and 
all the places which pass under this mark will have the 
sun vertical on that day. 

Secondly. Elevate the north or south pole, accor¬ 
ding as the sun’s declination is north or south, so many 
degrees above the horizon as are equal to the sun’s de¬ 
clination ; turn the globe on its axis from west to east; 
then, to those places which do not descend below the 
horizon, in that frigid zone near the elevated pole, the 
sun does not set on the given day : and to those places 
which do not ascend above the horizon, in that frigid 
zone adjoining to the depressed pole, the sun does not 
rise on the given day. 

OR, BY THE ANALEMMA. 

Bring the analemma to that part of the brass meridi¬ 
an which is numbered from the equator towards the 
poles, the degree directly above the day of the month, 
on the brass meridian, is the sun’s declination. Elevate 
the north or south pole, according as the sun’s declina¬ 
tion is north or south, so many degrees above the hori¬ 
zon as are equal to the sun’s declination ; turn the globe 
on its axis from west to east, then to those places which 
pass under the sun’s declination on the brass meri¬ 
dian, the sun will be vertical ; to those places (in that 


J98 


PIlOBLJilMS PERBORMEI) BY 


frigid zone near tlie elevated pole) which do not go be¬ 
low the horizon, the sun does not set ; and to those pla¬ 
ces (in that frigid zone near the depressed pole) which 
do not come above the horizon, the sun does not rise on 
the given day. 

Examples. 1. Find all the places of the earth where 
the sun is vertical on the 11th of May, those places in 
the north frigid zone where the sun does not set, and 
those places in the south frigid zone where he does not 
rise. 

Answer. The sun is vertical at St. Anthony, one of the Cape Verd 
islands, the Virgin Islands, south of St. Domingo, Jamaica, Golconda, 
kc. All places within eighteen degrees of the north pole will have 
constant day ; and those (if any) within eighteen degrees of the south 
pole will have constant night. 

2. Does the sun shine over the north or south 
pole on the 27'th of October ? To what places will he 
be vertical at noon ? What inhabitants of the earth will 
have the sun below their horizon during several revolu¬ 
tions, and to what part of the globe will the sun never 
set on that day ? 

3. Find all the places of the earth where the inhabi¬ 
tants have no shadow when the sun is on their meridian, 
on the first of June ? 

4. .What inhabitants of the earth have their shadows 
directed to every point of the compass, during a revolu¬ 
tion of the earth on its axis, on the 15th of July ? 

5. How far does the sun shine over the south pole on 
the 14th of November ? What places in the north frigid 
zone are in perpetual darkness ? And to what places is 
the sun vertical ? 

6. If the sun be vertical at any place on the 15th of 
April, how many days will elapse before he is vertical 
a second time at that place ? 

r. If the sun be vertical at any place on the 20th of 
August, how many days will elapse before he is vertical 
a second lime at that place ? 

8. Find all places of the earth where the moon 
will be vertical on the 15th of May, 1813.* 


* To perform this example, find the moon’s declination on the given 
day in the Nautical Almanac, or White’s Ephemeris, and mark it on 
the brass meridian , all places passing under that degree of declination 
will have the moon vertical, or nearly so, on the given day. The moon’s 
declination at midnight on the 15th of May, 1813, is 15° 46' south. 



THE TERRESTRIAL GLOBE. 


199 


PROBLEM XXIV. 

A place being given in the torrid sone, to find those 
two days of the year on which the siin will be vertical 
at that place. 


Rule. Bring the given place to that part of the brass 
meridian which is numbered from the equator towards 
the poles, and mark its latitude; turn the globe on its 
axis, and observe what two points of the ecliptic pass 
under that latitude ; seek those points of the ecliptic in 
the circle of signs, on the horizon, and exactly against 
them, in the circle of months, stand the days required. 

OR, BY THE ANALEMMA. 


Find the latitude of the given place (by Problem T.) 
and mark it on the brass meridian; bring the analemma 
to the brass meridian, upon which, exactly under the 
latitude, will be found the two days required. 

Examples. 1. On what two days of the year will the 
sun be vertical at Madras ? 

Answer. On the 25th of April and on the 18th of August. 

2. On what two days of the year is the sun vertical at 
the following places? 


O’why’hee 
Friendly Isles 
Straits of Alass 
Penang 
Trincomale 


St. Helena 
Rio Janeiro 
Quito 
Burbadoes 
Porto Bello 


Sierra Leone 
Vera Cruz 
Manilla 
Tinian Isle 
Pelew Islands 


PROBLEM XXV. 


The month and the day of the month being given (at 
any place not in the f rigid zones,) to find what other 
day of the year is of the same length. 

Rule. Find the sun’s place in the ecliptic for the 
given day (by Problem XX.) bring it to the brass me¬ 
ridian and observe the degree above it ; turn the globe 
on its axis till some other point of the ecliptic falls un¬ 
der the same degree of the meridian ; find this point of 




200 


PROBLEMS PERFORMED BY 


the ecliptic on the horizon, and directly against it you 
will find the day of the month required. 

This proDlem may be performed by the celestial globe in the same 
manner. 


OR, BY THE ANALEMMA. 

Look for the given day of the month on the analemma, 
and adjoining to it you will find the required day of the 
month. 


OR, WITHOUT A GLOBE. 

Any two days of the year which are of the same 
length, will be an equal number of days from the longest 
or shortest day. Hence, whatever number of days the 
given day is before the longest or shortest day, just so 
many days will the required day be after the longest or 
shortest day, et contra. 

Examples. 1 . What day of the year is of the same 
length as the 25th of April T 

Answer. Tbe 18tb of August. 

2. What day of the year is of the same length as the 
25(h of May ? 

3. If the sun rise at four o’clock in the morning at 
London on the ITth of July, on what other day of the 
year will he rise at the same hour ? 

4. If the sun set at seven o’clock in the evening at 
London on the 24th of August, on what other day of the 
year will he set at the same hour ? 

5. If the sun’s meridian altitude be 90° at Trinco* 
male, in the island of Ceylon, on the 12th of April, on 
what other day of the year will the meridian altitude be 
the same ? 

6. If the sun’s meridian altitude at London, on the 
25th of April, be 51° 35', on what other day of the year 
will the meridian altitude be the same ? 

PROBLEM XXVI. 

The months day, and hour of the day being giveUf io 

find where the sun is vertical at that instant. 

Ride. Find the sun’s declination (by Problem XX ) 
and mark it on the brass meridian ; bring the given 


THE TERRESTRIAL GLOBE. 


201 


place to the brass meridian, and set the index of the hour 
circle to twelve ; then, if the given time be before noon, 
turn the globe westward as many hours as it wants of 
noon ; but, if the given time be past noon, turn the globe 
eastward as many hours as the time is past noon ; the 
place exactly under the degree of the sun’s declination 
will be that sought. 

Examples. 1. When it is forty minutes past six 
o’clock in the morning at London on the 25th of April, 
where is the sun vertical ? 

Answer. Here the given time is five hours twenty minutes before 
noon ; hence, the globe must be turned towards the W'est till the index 
has passed over five hours and twenty minutes,* and under the sun’s de¬ 
clination, on the brass meridian, you will find Madras, the place required. 

2. When it is four o’clock in the afternoon at London, 
on the 18th of August, where is the sun vertical T 

Answer. Here the given time is four hours past noon ; hence, the 
globe must be turned towards the east, till the index has passed over 
four hours ; then under the sun’s declination, you will find Barbadoes, 
the place required. 

3. When it is three o’clock in the afternoon at Lon¬ 
don, on the 4th of January, where is the sun vertical ? 

4. When it is three o’clock in the morning at Lon¬ 
don, on the 11th of April, where is the sun vertical ? 

5. When it is thirty-seven minutes past one o’clock in 
the afternoon at the Cape of Good Hope, on the 5th of 
February, where is the sun vertical ? 

6. When it is eleven minutes past one o’clock in the 
afternoon at London, on the 29th of April, where is the 
sun vertical ? 

7. When it is twenty minutes past five o’clock in the 
afternoon at Philadelphia, on the 18th of May, where is 
the sun vertical ? 

8. When it is nine o’clock in the morning at Calcutta, 
on the 11th of April, where is the sun vertical ? 


* If the hour circle be not divided to twenty minutes, turn the globe 
westward till the index has passed over five hours and a quarter ; then 
by turning it a degree and a quarter farther to the west (answering to 
five minutes of time) the solution will be exact. See the note to the 
next problem. The degrees must be couated on the equator. 


28 



202 PROBLEMS PERFORMED BY 

PROBLEM XXVIl. 


The monlhy day, and hour of the day at any place being 
given, to jind all those places oj the earth rvhere the 
sun is rising, those places where the sun is setting, 
tho^e places that have noon, that particular place 
where the sun is vertical, those places that have morn¬ 
ing twilight, those places that have evening twilight, 
and those places that have midnight* 


Rule, Find the sun’s declination (by Problem XX.) 
and mark it on the brass meridian ; elevate the north or 
south pole, according as the sun’s declination is north or 
south, so many degrees above the horizon as are equal 
to the sun’s declination; bring the given place to the 
brass meridian, and set the index of the hour circle to 
twelve; then, if the given time be before noon, turn the 
globe westward as many hours as it wants of noon ; but, 
if the given time be past noon, turn the globe eastward 
as many hours as the time is past noon ; keep the globe 
in this position ; then all places along the western edge 
of the horizon have the sun rising ; those places along 
the eastern edge have the sun setting; those under the 
brass meridian, above the horizon, have noon; that par¬ 
ticular place which stands under the sun’s declination on 
the brass meridian has the sun vertical; all places below 
the western edge of the horizon, within eighteen degrees, 
have morning twilight; those places which are below the 
eastern edge of the horizon, within eighteen degrees, 
have evening twilight; all places under the brass meri¬ 
dian, below the horizon, have midnight; all the places a- 
bove the horizon have day, and those below it have night, 
or twilight. 

Examples. 1. When it is fifty-two minutes past four 
o’clock in the morning at London, on the fifth of March, 
find all places of the earth where the sun is rising, set¬ 
ting, &c. 

Answer. The sun’s declination will be found to be south ; there¬ 
fore, elevate th** south pole 6;^® above the horizon. The given time be¬ 
ing seven hours eight minutes before noon (=12 h. —4 h. 52 ra.) the 
globe must be turned towards the west till the index has passed over 


tirti TERRESTRIAL GLOBE. 203 

*even hours eiglit minutes.* Let the globe be fixed in this position ; 
then. 

The sun is rising at the western part of the White Sea, Petersburg, 
the Morea in I'urkey, &c. 

Setting at the eastern coast of Kamtschatka, Jesus island, Palmerston 
island, &:c. between the Friendly and Society islands. 

Noon at the lake Baikal in Irkoutsk, Cochin China, Cambodia, Sun- 
da islands, &:c. 

Vertical at Batavia. 

Morning twilight at Sweden, part of Germany, the southern part of 
Italy, Sicily, the western coast of Africa along the Ethiopian Ocean, 
&c. 

Evening twilight at the north west extremity of North America, 
the Sandwich islands, Society islands, drc. 

Midnight at Labrador, New-York, western part of St. Domingo, 
Chili, and the western coast of South America. 

Day at the eastern part of Russia in Europe, Turkey, Egypt, the 
Cape of Good Hope, and all the eastern part of Africa, almost the 
whole of Asia, &c. 

Night at the whole of North and South America, the western part 
of Africa, The British isles, France, Spain, Portugal, &c. 

2. When it is four o’clock in the afternoon at Lon¬ 
don, on the 251h of April, where.is the sun rising, set¬ 
ting, &c. See. ? 

Answer. The sun’s declination being north, the north pole must 
be elevated l3° above the horizon ;t and as the given time is four 
o’clock in the afternoon, the globe must be turned four hours towards 
the east; then the sun will be rising at O’why’hee, &c. setting at the 
Cape of Good Hope, &c. it will be noon at Buenos Ayres, &c.; the sun 
will be vertical at Barbadocs; and following the directions in the prob¬ 
lem, all the other places are readily found. 

3. When it is ten o’clock in the morning at London, 
on the longest day, to what countries is the sun rising, 
setting, &c. &c. ? 

4. When it is ten o’clock in the afternoon at Botany 
Bay, on the 15th of October, where is the sun rising, set¬ 
ting, &c. &c. ? 

5. When it is seven o’clock in the morning at Wash¬ 
ington, on the 17th of February, where is the sun rising, 
setting, &c. &c. ? 


* The hour circles, in general, are not divided into parts less than 
a quarter of an hour, but the odd minutes are easily reckoned. In this 
example having turned the globe westward till the index has passed 
over seven hours ; then, because four minutes of time make one degree, 
reckon two degrees on the equator eastward, and turn the globe till 
they pass under the brass meridian. 

t If the hour circle of the globe be placed above the brass meridian, 
it must be unscrewed and removed from the pole ; the hours may then 
be counted on the equator.—See the note to definition 18, page 5. 



204 


PROBLEMS PERFORMED BY 


6. When it is midnight at the Cape of Good Hope, 
on the 2rth of where is the son rising, setting, 

&c. cScc. ? 

PROBLEM XXVIII. 

To find the time of the su7i^s rising and setting, and 

the length of the day and flight at any place. 

Rule, Find the sun’s declination (bj Problem XX.) 
and elevate the north or south pole, according as the de¬ 
clination is north or south, so many degrees above the 
horizon as are equal to the sun’s declination ; bring the 
given place to the brass meridian, and set the index of 
the hour circle to twelve; turn the globe eastward till 
the given place comes to the eastern semi-circle of the 
horizon, and,the number of hours passed over by the index 
will be the time of the sun’s setting : deduct these hours 
from twelve, and you have the time of the sun’s rising ; 
because the sun rises as many hours before twelve as it 
sets after twelve. Double the time of the sun’s setting 
gives the length of the day, and double the time of ris¬ 
ing gives the length of the night. 

By the same rule, the length of the longest day, at all places not in 
the frigid zones, may be readily found : for the longest day at all pla¬ 
ces in north latitude is on the 21st of June, or when the sun enters Can¬ 
cer : and the longest day at all places in south latitude is on the Slst of 
December, or when the sun enters the sigq Capricorn. 

OR, 

Find Ihe latitude of the given place, and elevate the 
north or south pole, according as the latitude is north or 
south, so many degrees above the horizon as are equal 
to the latitude ; find the sun’s place in the ecliptic (by 
Problem XX.) bring it to the brass meridian, and set 
the index of the hour circle to twelve; turn the globe 
westward till the sun’s place comes to the western semi¬ 
circle of the horizon, and the number of hours passed 
over by the index will be the time of the sun’s setting ; 
and these hours taken from twelve will give the time 
of rising: then, as before, double the time of setting 
gives the length of the day, and double the time of rising 
gives the length of the night. 


THE TERRESTKIAL GLOBE. 


20.0 


OR, BY THE ANALEMMA. 

Find the latitude of the given place, and elevate the 
north or south pole, according as the latitude is north or 
south, the same number of degrees above the horizon ; 
bring the middle of the analemma to the brass meridian, 
and set (he index of the hour circle to twelve ; turn the 
globe westward till the day of the month on the analem¬ 
ma comes to the western semi-circle of the horizon, and 
the number of hours passed over by the index, will be 
the time of the sun’s setting, &c. as above. 

Examples. 1. What time does the sun rise and set 
at London on the 1st of June, and what is the length of 
the day and night ? 

Answer The sun sets aj 8 min. past 8, and rises 52 min. past S. 
the len^rth of the day is 16 hours 16 minutes, and the length of the night 
7 hours 44 minutes. The learner will readily perceive that, if the time 
at which the sun rises be given, the time at which it sets, together with 
the length of the day and night, may be found without a globe; if the 
length of the day be given, the length of the night, aud the time the 
sun rises and sets, may be found; if the length of the night be given, 
the length of the day and the time the sun rises and sets are easily 
know'n 

2. At what time does the sun rise and set at the 
following places, on the respective days mentioned, and 
what is the length of the day and night ? 


London, iTth of May 
Gibraltar, 22d of July 
Edinburgh, 29tb January 
Botany Bay, 20th Feb’ry 
Pekin, 20th April 


Cape of Good Hope, 7 Dec. 
Cape Horn, 29th January 
Washington, 15lh December 
Petersburg, 24th October 
Constantinople, 18th August. 


3. Find the time the sun rises and sets at every place 
on the surface of the globe, on the 2lBt of March, and 
likewise on the 23d of September. 

4. Required the length of the longest day and short¬ 
est night at the following places: 

London Paris Pekin 

Petersburg Vienna Cape Horn 

Aberdeen Berlin Washington 

Dublin Buenos Ayres Cape of Good Hope 

Glasgow Botany Bay Copenhagen. 

Required the length of the shortest day and longest 
night at the following places : 



20G 


PROBLEMS PERFORMED BV 


London 
Archangel 
O Taheitee 
Quebec 


Lima 
Mexico 
St. Helena 
Alexandria 


Paris 

O’why’hee 

Lisbon 

Falkland Islands. 


6. How much longer is the 21st of June at Peters¬ 
burg than at Alexandria ? 

7. How much longer is the 21st of December at Alex¬ 
andria than at Petersburg ? 

8. At what time does the nun rise and set at Spitz- 
bergen on the 5th of April ? 

PROBLEM XXIX. 

The length of the day at any place being given, to find 
the sim^s declination, and the day of the month. 


Rule. Bring the given place to the brass meridian, 
and set the index to twelve ; turn the globe eastward till 
the index has passed over as many hours as are equal to 
half the length of the day ; keep the globe from revolv¬ 
ing on its axis, and elevate or depress one of the poles, 
till the given place exactly coincides with the eastern 
semi-circle of the horizon ; the distance of the elevated 
pole from the horizon will be the sun’s declination : mark 
the sun’s declination, thus found, on the brass meridian: 
turn the globe on its axis, and observe what two points 
of the ecliptic pass under this mark ; seek those points 
in the circle of signs on the horizon, and exactly against 
them, in the circle of months, stand the days of the 
months required. 

OR, 

Bring the meridian passing through Libra* to coincide 
with the brass meridian, elevate the pole to the latitude 
of the place, and set the index of the hour circle to 
twelve; turn the globe eastward till the index has pass¬ 
ed over as many hours as are equal to half the length of 
the day, and mark where the meridian, passing through 


* Any meridian will answer the purpose, and the globe maybe turn¬ 
ed either eastward or westward; but it is the most convenient to turn, 
it eastwai'd, because the brass meridian is graduated on the east side.^ 



THE TERRESTRIAL GLOBE. 


207 


Libra, is cut by the eastern semi-circle of the horizon ; 
bring this mark to the brass meridian,* and the degree 
above it is the sun’s declination; with which proceed as 
above. 


OR, BY THE ANALEMMA. 

Bring the middle of the analernma to the brass meri¬ 
dian, elevate the pole to the latitude of the place, and set 
the index of the hour circle to twelve; turn the globe 
eastward till the index has passed over as many hours as 
are equal to half the length of the day : the two days, on 
the analernma, which are cut by the eastern semi-circle 
of the horizon, will be the days required ; and, by bring¬ 
ing the analernma to the brass meridian, the sun’s decli¬ 
nation will stand exactly above these days. 

Examples. 1 . What two days in the year are each 
sixteen hours long at London, and what is the sun’s de¬ 
clination T 

Answer. The24tli of May and the 17th of July. The sun’s decli¬ 
nation is about north. 

2. What two days of the year are each fourteen hours 
long at London ? 

3. On what two days of the year does the sun set at 
half past seven o’clock at Edinburgh ? 

4. On what two days of the year does the sun rise at 
four o’clock at Petersburg ? 

5. What two nights of the year are each ten hours long 
at Copenhagen ? 

6. What day of the year at London is sixteen hours 
and a half long ^ 

PROBLEM XXX. 

To find the length of the longest dap at any place in the 

norihf frigid zone. 

Rule. Bring the given place to the northern point of 
the horizon (by elevating or depressing the pole,) and ob- 


* If Adams’globes be used, the meridian passing through Libra is 
graduated like the brass meridian, and the declination is found at once. 

t The south frigid zone is uninhabited (at least we know of no in¬ 
habitants) the problem is not applied to that zone ; however, the rule 
is general, reading south for north, and 21st of December for the 21st 
of June. 



208 


rilOBLEMS PEKFOUMEB BY 


serve its distance from the north pole on the brass me¬ 
ridian ; count the same number of degrees on the brass 
meridian trom the equator, towards the north pole, and 
mark the place where the reckoning ends ; turn the 
globe on its axis, and observe what two points of the 
ecliptic pass under the above mark ; find those points of 
the ecliptic in the circle of signs on the horizon, and ex¬ 
actly against them, in the circle of months, ^ou will find 
the days on which the longest day begins and ends. 
The day preceding the 21st of June is that on which 
the longest day begins at the given place, and the day 
following the 21st of June is that on which the longest 
day ends ; the space of time between these days is the 
length of the longest day. 

OR, BY THE ANALEMMA. 

Bring the given place to that part of the brass meri¬ 
dian which is numbered from the north pole towards the 
equator, and observe its distance in degrees from the 
pole ; count the same number of degrees on the brass 
meridian from the equator towards the north pole, and 
mark where the reckoning ends; bring the analemma to 
the brass meridian, and the two days which stand under 
the above mark will point out the beginning and end of 
the longest day. 

Examples. 1. What is the length of the longest day 
at the North Cape, in the island of Maggeroe, in latitude 
71° 30' north? 

Answer. The place is 18^® from the pole; the longest day begins 
on the 14th of May, and ends on the SOth of July; the day is therefore 
seventy-seVen days long, that is, the sun does not set during seventy- 
seven revolutions of the earth on its axis. 

2^ What is the length of the longest day in the 
north of Spitzbergen, and on what days does it begin and 
end ? 

3. What is the length of the longest day at the north-- 
ern extremity of Nova Zembla? 

4. What is the length of the longest day at the north 
pole, and on what days does it begin and end ? 


THE TERRESTRIAL GLOBE. 


209 


PROBLEM XXXI. 

To find the length of the longest night at any place in 

the north"^ frigid zone. 

Rule, Bring the given place to the northern point 
of the horizon (by elevating or depressing the pole,) and 
observe its distance from the north pole on the brass me¬ 
ridian j count the same number of degrees on the brass 
meridian from the equator towards the south pole, and 
mark the place where the reckoning ends ; turn the 
globe on its axis, and observe what two points of the 
ecliptic pass under the above mark; find those points of 
the ecliptic in the circle of signs in the horizon, and ex¬ 
actly against them, in the circle of months, you will find 
the days on which the longest night begins and ends. 
The day preceding the 21st of December is that on 
which the longest night begins at the given place, and 
the day following the 21st of December is that on which 
the longest night ends : the space of time between these 
days is the length of the longest night. 

OR, BY THE ANALEMMA. 

Bring the given place to that part of the brass meri¬ 
dian which is numbered from the north pole towards the 
equator, and observe its distance in degrees from the 
pole ; count the same number of degrees on the brass 
meridian from the equator towards the south pole, and 
mark where the reckoning ends ; bring the analemma to 
the brass meridian, and the two days which stand under 
the above mark will point out the beginning and end of 
the longest night. 

Examples, 1. What is the length of the longest 
night at the North Cape, in the island of Maggeroe, in 
latitude 71°30' north? 


* This problem is equally applicable to any place in th« south frigid 
zone, and the rule will be general by reading south for north, arid the 
contrary; likewise, instead of the 21st of December read the 21st of 
June. 

29 



210 


PROBLEMS PERFORMED BY 


Answer. Tbe place is 18^° from the pole; the longest night begins 
on the l6th of November, and ends on the i^Tth of January ; the night 
is therefore, seventy-three days long, that is, the sun does not rise dur¬ 
ing seventy-three revolutions of the earth on its axis. 

2. W hat is the length of the longest night at the north 
of Spilzbergen ? 

3. The Dutch wintered in Nova Zembla, latitude 76 
degrees north, in the year 1596 : on what day of the 
month did they lose sight of the sun; on what day of the 
month did he appear again ; and how many days were 
they deprived of his appearance, setting aside the effect 
of refraction ? 

4. For how many days are the inhabitants of the 
northernmost extremity of Russia deprived of a sight of 
the sun ? 


PROBLEM XXXII. 

To find the number of days which the sun rises and sets 

at atiy place in the north^ frigid zone. 

Rule* Bring the given place to the northern point 
of the horizon (by elevating or depressing the pole,) and 
observe its distance from the north pole on the brass 
meridian ; count the same number of degrees on the 
brass meridian from the equator towards the poles north¬ 
ward and southward, and make marks where the reck¬ 
oning ends ; observe what two points of the ecliptic 
nearest to Aries, pass under the above marks ; these 
points will show (upon the horizon) the end of the long¬ 
est night and the beginning of the longest day ; during 
the time between these days the sun will rise and set 
every twenty-four hours ; next, observe what two points 
of the ecliptic, nearest to Libra, pass under the marks 
on the brass meridian ; find these points, as before, in 
the circle of signs, and against them you will find the 
day on which the longest day ends at the given place, 
and the day on which the longest night begins ; during 
the time between these days the sun will rise and set 
every twenty-four hours. 


* The same might be found for a place in the south frigid zone, were 
that zone inhabited. 



THE TERRESTRIAL GLOBE, 


2Ji 


OR, 

Find the length of the longest day at the given place, 
(by Prob. XXX.) and the length of the longest night 
(by Prob. XXXI.,) add these together, and subtract 
the sum from 365 days, the length of the year, the re¬ 
mainder will show the number of days which the sun 
rises and sets at that place. 


OR, BY THE ANALEMMA. 


Find how many degrees the given place is from the 
north pole, and mark those degrees upon the brass me¬ 
ridian on both sides of the equator : observe what four 
days on the analemma stand under the marks on the 
brass meridian ; the time between those two days on the 
left hand part of the analemma (reckoning towards the 
north pole) will be the number of days on which the 
sun rises and sets, between the end of the longest night 
and the beginning of the longest day ; and the time be¬ 
tween the two days on the right hand part of the analem¬ 
ma (reckoning towards the south pole) will be the num¬ 
ber of days on which the sun rises and sets, between the 
end of the longest day and the beginning of the longest 
night. 

Examples, 1. How many days in the year does the 
sun rise and set at the North Cape, in the island of Mag- 
geroe, in latitude 71° 30' north ? 

Answer. The place is 18^® from Jthe pole, the two points in the 
ecliptic, nearest to Aries, which pass under 18^° on the brass meridian, 
are 8® in answering to the SiTtb of January, and 24° in ^, answer¬ 
ing to the I4th of May. Hence, the sun rises and sets for 107 days, 
viz. from the end of the longest night, which happens on the 27th of 
January, to the beginning of the longest day, which happens on the 14th 
of May. Secondly, the two points in the ecliptic, nearest to Libra, 
which pass under 18^° on the brass meridian, are 8® in <Y>, answering to 
the SOthof July, and 24° in n^, answering to the 15th of November. 
Hence, the sun rises and sets for 108 days, viz from the end of the long¬ 
est day, w'hich happ^s on the 30th of July, to the beginning of the 
longest night, which happens on the 15th of November; so that the 
whole time of tlie sun’s rising and setting is 215 days. 


PllOBLEMS PERFORMED BY 




OR, THUS: 

The length of the longest day, by Example Ist, Prob XXX. is 7T 
days; the length of the longest night, by Example 1st Prob. XXXI. 
is 73 days ; the sura of these is 150, which deducted from 365, leaves 
215 days as above. 

2. How many days in the year does the sun rise and 
set at the north of Spitzbergen ? 

3. How many days does the sun rise and set at Green¬ 
land, in latitude 75° north ? 

4. Now many days does the sun rise and set at the 
northern extremity of Russia in Asia? 

PROBLEM XXXIII. 

To find in what degree of north latitude, on any day 
between the 2\st of March and the 2\st of June, or in 
what degree of south latitude, on any day between the 
23d of September and the 21st of December, the sun 
begins to shine constantly without setting ; and also 
in what latitude in the opposite hemisphere he begins 
to be totally absent. 

Rule, Find the sun’s declination (by Prob. XX.) 
and count the same number of degrees from the north 
pole towards the equator, if the declination be north, or 
from the south pole, if it be south, and mark the point 
where the reckoning ends ; turn the globe on its axis, 
and all places passing under this mark are those in which 
the sun begins to shine constantly without setting at that 
time : the same number of degrees from the Contrary 
pole will point out all the places where twilight or total 
darkness begins. 

Examples. 1. In what latitude north, and at what 
places, does the sun begin to shine without setting, dur¬ 
ing several revolutions of the earth on its axis, on the 
14lh of May ? 

Answer. The sun’s declination is 18^’ north, therefore, all places in 
latitude 71^® north will be the places sought, viz. the North Cape in 
Lapland, the southern part of Nova Zembla, Icy Cape, &c. 

2. In what latitude south does the sun begin to shine 
without setting on the 18th of October, and in what lati¬ 
tude north does he begin to be totally absent ? 


the terrestrial globe. 


213 


Answer. The sun’s declination is 10° south, therefore, he begins to 
shine constantly in latirt de 80° south, where there are no inhabitants 
known, and to be totally absent in latitude 80° north, viz. at Spitzber- 
gen. 

3. In what latitude does the sun begin to shine with¬ 
out getting on the 20th of April ? 

4. In what latitude north does the sun begin to shine 
without setting on the 1st of June, and in what degree 
of south latitude does it begin to be totally absent ? 

PROBLEM XXXIV. 


Any number of days, not exceeding 182, being given, 

to find the parallel of north latitude in which the sun 

does not set for that time. 

Rule, Count half the number of days from the 21st 
of June on the horizon, eastward or westward, and op¬ 
posite to the last day you will find the sun’s place in the 
circle of signs; look for the sign and degree on the eclip¬ 
tic, which bring to the brass meridian, and observe the 
sun’s declination ; reckon the same number of degrees 
from the north pole (on that part of the brass meridian 
which is numbered from the equator towards the poles) 
and you will have the latitude sought. 

Examples, 1, In what degree of north latitude, and 
at what places, does the sun continue above the horizon 
for seventy-seven days ? 

Answer. Half the number of days is 38^, and if reckoned backward, 
or towards the east, from the 21st of June, will answer to the 14th of 
May; and if counted forward, or towards the w'est, will answ’er to the 
30th of July ; on either of which days the sun’s declination is 18^ de¬ 
grees north, consequently, the places sought are 18^ degrees from the 
north pole, or in latitude 71^ degrees north; answering to the North 
Cape in Lapland, the south part of Nova Zembla, Icy Cape, &c. 

2. In what degree of north latilude is the longest day 
134 days, or 3216 hours in length ? 

3. In what degree of north latitude does the sun con¬ 
tinue above the horizon for 2160 hours ? 

4. In what degree of north latitude does the sun con¬ 
tinue above the horizon for 1152 hours ? 


211 


PROBLEMS PERFORMED BY 


PROBLEM XXXV. 

To find the beginning, end, and duration of twilight 

at any place, on any given day. 

Rule, Find the sun’s declination for the given day 
(by Problem XX.) and elevate the north or south pole, 
according as the declination is north or south, so many 
degrees above the horizon as are equal to the sun’s de¬ 
clination ; screw the quadrant of altitude on the brass 
meridian, over the degree of the sun’s declination ; bring 
the given place to the brass meridian, and set the index 
of the hour circle to twelve ;turn the globe eastward till 
the given place comes to the horizon, and the hours pass¬ 
ed over by the index will show the time of the sun’s set¬ 
ting, or the beginning of evening twilight; continue the 
motion ot the globe eastward, till the given place coin¬ 
cides with 18° on the cjuadrant of altitude below* the 
horizon, the space passed over by the index of the hour 
circle from the time of the sun’s setting, will show the 
duration of evening twilight. The morning twilight is 
the same length. 


OR, THUS : 

Elevate the north or south pole, according as the lati¬ 
tude of the given place is north or south, so many de¬ 
grees above the horizon as are equal to the latitude ; find 
the sun’s place in the ecliptic, bring it to the brass meri¬ 
dian, set the index of the hour circle to twelve, and 
screw the quadrant of altitude upon the brass meridian 
over the given latitude; turn the globe westward on its 
axis till the sun’s place comes to the western edge of the 
horizon, and the hours passed over by the index will 
show the time of the sun’s setting, or the beginning of 
evening twilight; continue the motion of the globe west¬ 
ward till the sun’s place coincides with 18° on the quad¬ 
rant of altitude below the horizon, the space passed over 
by the index of the hour circle, from the time of the sun’s 
setting, will show the duration of evening twilight. 


* The quadrant of altitude belonging to our modern globes is always 
graduated to 18 degrees below the horizon. 



THE TERRESTRIAL GLOBE. 


215 


OR, BY THE ANALEMMA. 

EJevate the pole to the latitude of the place, as above, 
and screw the quadrant of altitude upon the brass meri¬ 
dian over the degree of latitude ; bring the middle of the 
analemmalo the brass meridian, and set the index of the 
hour circle to twelve : turn the globe westward till the 
given day of the month on the analemma comes to the 
western edge of the horizon, and the hours passed over 
by the index will show the time of the sun’s setting, or 
the beginning of evening twilight : continue the motion 
of the globe westward till the given day of the month 
coincides with 18° on the quadrant below the horizon, 
the space passed over by the index, from the time of the 
sun’s setting, will show the duration of evening twilight. 

Examples, 1. Required the beginning, end, and du¬ 
ration of morning and evening twilight at London, on 
the 19th of April. 

Answer. The sun sets at two minutes past seven, and evening twi¬ 
light ends at nineteen minutes past nine : consequently, morning twi¬ 
light begins at (12 h.—9 h. 19 m.=) 2 h. 41 m. and ends at (12 h.— 
7 h.2 m. =) 4 h. 58 m. ; the duration of twilight is 2 hours i7 minutes. 

2. What is the duration of twilight at London on the 
23d of September ? what time does dark night begin ? and 
at what time does day break in the morning ? 

Answer. The sun sets at six o’clock, and the duration of twilight is 
two hours; consequently, the evening twilight ends at eight o’clock, 
and the morning twilight begins at four. 

3. Required the beginning, end, and duration of 
morning and evening twilight at London, on the 25th of 
August. 

4. Required the beginning, end, and duration of 
morning and evening twilight at Edinburgh, on the 20th 
of February. 

5. Required the beginning, end, and duration of morn¬ 
ing and evening twilight at Cape Horn, on the 20th of 
February. 

6. Required the beginning, end, and duration of 
morning and evening twilight at Madras, on the 15th of 
.Tune. 


216 


PROBLEMS performed BY 


PROBLEM XXXVI. 


To find the beginningy end, and duration of constant 
day or twilight at any place. 


Rule. Find the latitude of the given place, and add 
18° to that latitude ; count the number of degrees cor¬ 
respondent to the sum, on that part of the brass meridian 
which is numbered from the pole towards the equa’or, 
mark where the reckoning ends, and observe what two 
points of the ecliptic pass under the mark ;* (hat point 
wherein the sun’s declination is increasing will show on 
the horizon the beginning of constant twilight ; and that 
point wherein the sun’s declination is decreasing, will 
show the end of constant twilight. 

Examples. 1. When do we begin to have constant 
day or twilight at London, and how long does it con¬ 
tinue ? 

Answer. The latitude of London is 51^ degrees north, to which add 
18 degrees, the sum is 69^, the two points of the ecliptic which pass 
under 69^ are two^degrees in Hi answering to the22d of May; and 29 
degrees in 25, answering to the 21st of July; so that, from the 22d of 
May to the 2l8t of July, the sun never descends 18 degress below the 
horizon of London. 

2. When do the inhabitants of the Shetland islands 
cease to have constant day or twilight ? 

3. Can twilight ever continue from sun-set to sun¬ 
rise at Madrid ? 

4. When does constant day or twilight begin at Spitz- 
bergen ? 

5. What is the duration of constant day or twilight at 
the North Cape in Lapland, and on what day, after their 
long winter’s night, does the sun’s rays first enter the at¬ 
mosphere ? 


* If, after 18 degrees be added to the latitude, the distance from the 
pole will not reach the eliptic. there will be no constant twilight at the 
given place : viz. to the given latitude add 18 degrees, and subtract the 
sum from 90, if the remainder exceed 23^ degrees, there can be no con¬ 
stant twilight at the given place. 



THE TERRESTRIAL GLOBE. 


217 


PROBLEM XXXVII. 


To find the duration of twilight at the north pole. 

Rule. Elevate the north pole so that the equator may 
coincide with the horizon; observe what point of the 
ecliptic, nearest to Libra, passes under 18° below (he 
horizon, reckoned on the brass meridian, and find the day 
of the month correspondent thereto; the time elapsed 
from the 23d of September to this time will be the du¬ 
ration of evening twilight. Secondly, observe what 
point of the ecliptic nearest to Aries, passes under 18° 
below the horizon, reckoned on the brass meridian, and 
find the day of the month correspondent thereto ; the 
time elapsed from that day to the 21st of March will be 
the duration of morning twilight. 

Example. What is the duration of twilight at the 
north pole, and what is the duration of dark night 
there ? 

A nswer. Th,e point of the ecliptic nearest to Libra which pa«:ges un¬ 
der 18 degrees below the horizon, is 22 degrees in Tt]^, answering to the 
ISth of November ; hence, the evening twilight continues from the 
25d of September (the end of the longest day) to the I3th of Novem¬ 
ber (the beginning of dark night) being 51 days. The point of the 
ecliptic nearest to Aries which passed under 18 degrees below the hori¬ 
zon is 9 degrees in answering to the 29th of January : hence, the 
morning twilight continues from the 29th of January to the 2l8t of 
March (the beginning of the longest day) being fifty-one days. From 
the 2Sd of September to the 21«t of March is 1T9 days, from which de¬ 
duct 102 (=51 V2,) the remainder is 77 days, the duration of total 
darkness at the north pole; but even during this short period, the moon 
and the Aurora Borealis shine with uncommon splendour. 

PROBLEM XXXVIII. 

To find in what climate any given place on the globe 
is situated. 

Rule. 1. If the place be notin the frigid zones, find 
the length of the longest day at that place (by problem 
XXVIII.) and subtract twelve hours therefrom ; the 
number of half hours in the remainder will show the c\U 
mate. 


218 


PKOBLEMS PERFORMED BY 


2. If the place be in the frigid zone,* find the length 
of the longest day at that place (by Problem XXX,) 
and if that be less than thirty days, the place is in ihe 
twenty-fifth climate, or the first within the polar circle ; 
if more than thirty and less than sixty, it is in the twen¬ 
ty-sixth climate, or the second wilhin the polar circle ; 
if more than sixty and less than ninety, it is in the twen¬ 
ty-seventh climate, or the third within the polar circle, 
Sec. 

Examples. 1. In what climate is London, and what 
other remarkable places are situated in the same cli¬ 
mate ? 

Answer. The longest day at London is 16^ hours, if we deduct 12 
therefrom, the remainder will be 4^ hours, or nine half hours ; hence, 
London is the 9th climate north of the equator ; and, as all places in 
or near the same latitude are in the same climate, w'e shall find Amster¬ 
dam, Dresden, Warsaw, Irkoutsk, the southern part of the peninsula of 
Kamtschatka, Nootka Sound, the south of Hudson’s Bay, the north of 
IVewfoundland, &c. to be the same climate as London.—The learner is 
requested to turn to the note to Definition 69th, page l.'i. 

2. In what climate is the North Cape in the island of 

Maggeroe, latitude 71° 30' north ? 

Answer. The length of the longest day is 77 days ; these days di¬ 
vided by 30, give two months for the quotient, and a remainder of 17 
days; hence, the place is in the third climate within the polar circle, 
or the 27th climate reckoning from the equator. The southern part of 
Nova Zembla. the northern part of Siberia, James* island, Baffin^s Bay, 
the northern part of Greenland, &c. are in the same climate. 

3. In what climate is Edinburgh, and what other 
places are situated in the same climate? 

4. In what climate is the north of Spitzbergen ? 

.0. In what climate is Cape Horn ? 


* The climates between the polar circles and the poles were unknown 
to the ancient geographers ; they reckoned only seven climates north 
of the equatbr. The middle of the first northern climate they made to 
pass through Meroe, a city of Ethiopia, built by Cambyses, on an island 
in the Nile, nearly under the tropic of Cancer; the second through 
Syene, a city of Thebais in upper Egypt, near the cataracts of 
theNile; the third through Alexandria ; the fourth through Rhodes; 
the fifth through Rome or the Hellespont; the sixth through the mouth 
of the Borysthenes or Dnieper, and the seventh through the Riphaean 
mountains, supposed to be situated near the source of the Tanais or 
Don river. The southern parts of the earth being in a great measure 
unknown, the climates received their names from the northern ones, 
?ind not from particular towns or places. Thus the climate which was 
supposed to be at the same distance from the equator southward, as 
Meroe was northward, was called Antidiameroes, or the opposite cli¬ 
mate to Meroe; Antidiasyenes was the opposite climate to Syenes, &c. 





THE TERRESTRIAL GLOBE, 219 

6. In what climate is Botany Bay, and what other 
places are situated in the same climate ? 

PROBLEM XXXIX. 

To find the breadths of the several climates between the 
equator and the polar circles* 

Rule. For the northern climates. Elevate the north 
pole 23|° above the northern point of the horizon, bring 
the sign Cancer to the meridian, and set the index to 
twelve; turn the globe eastward on its axis till the index 
has passed over a quarter of an hour ; observe that par¬ 
ticular point of the meridian passing through Libra, 
which is cut by the horizon, and at the point of inter¬ 
section make a mark with a pencil; continue the motion 
of the globe eastward till the index has passed over a- 
nother quarter of an hour, and make a second mark ; 
proceed thus till the meridian passing through Libra^ 
will no longer cut the horizon ; the several marks brought 
to the brass meridian will point out the latitude where 
each climate ends, f 

Examples. 1. What is the breadth of the ninth north 
climate, and what places are situated within it ? 

Answer. The breadth of the 9ih climate is 2° 57', it begins in lati¬ 
tude 49® 2' north, and ends in latitude 51° 59' north, and all places situa¬ 
ted within this space are in the same climate. The places will be nearly 
the same as those enumerated in the first example to the preceding 
problem. 

2. What is the breadth of (he second climate, and in 
what latitude does it begin and end ? 

3. Required the beginning, end, and breadth of the 
fifth dimate. 

4. What is the breadth of the seventh Climate north 
of the equator ? In what latitude does it begin and end, 
and what places are situated within it ? 


♦ On Adams* globes, the meridian passing through Libra is divided into 
degrees, in the same manner as the brass meridian is divided; the horh 
zon will, therefore, cut this meridian in the several degree answering 
to the end of each climate, without the trouble of bringing it to the 
brass meridian, or marking the globe. 

t See a table of the climates, with the method of constructing it, at 
pages 16 and 17. 



220 


PROBLEMS PERFORMED BY 


PROBLEM XL. 

To find that part of the equation of time which depends 
upon the obliquity of the ecliptic. 

Rule. Find the sun’s place in the ecliptic, and bring 
it to the brass meridian ; count the number of degrees 
from Aries to the brass meridian, on the equator and on 
the ecliptic; the difference, reckoning four minutes of 
time to a degree, is the equation of time. If the number 


Note. The equation of time, or differ¬ 
ence beween the time shown by a well 
regulated clock, and a true sun-dial de¬ 
pends upon two causes; viz. the obliqui¬ 
ty of the ecliptic, and the unequal mo¬ 
tion of ihe earth in its orbit. The for¬ 
mer of these causes may be explained by 
the above problem. If two suns were to 
set off at the same time from the point A- 
ries, and move over equal places in equal 
time, the one on the ecliptic, the other 
on the equator, it is evident they would 
never come to the meridian together, 
except at the time of the equinoxes, 
and on the longest and shortest days. 
The annexed Table shows how much 
the sun is faster or slower than the 
clock ought to be, so far as the varia¬ 
tion depends on the obliquity of the e- 
cliptic only. The signs of the first and 
third quadrants of the ecliptic are at the 
top of the table and the degrees in 
these signs on the left hand ; in any of 
these signs the sun is faster than the 
clock. The signs of the second and 
third quadrants are at the bottom of the 
table, and the degrees in these signs at 
the right hand ; in any of these signs 
the sun is slower than the clock. 

Thus, when the sun is in W degrees 
of E or nh, it is 9 minutes 50 seconds 
faster than the clock, and, when the 
sun is in 18 degrees of 05 or >5 it is 
6 minutes 2 seconds slower than the 
clock. 


'^un faster than the 

clock in 

bC 

T 

1 



a 

1 Q,u 

ft 

-ru 



t 

SQ.U 


M.S. 

MS 


1.3. 


0 

0 

0 

8 

24 

8 

46 

30 

1 

0 

20 

8 

35 

8 

36 

29 

2 

0 

40 

8 

45 

8 

25 

28 

3 

1 

0 

8 

54 

8 

14 

27 

4 

1 

19 

9 

3 

8 

1 

26 

5 

1 

39 

9 

11 

7 

49 

25 

6 

1 

59 

9 

18 

7 

35 

24 

7 

2 

18 

9 

24 

7 

21 

23 

8 

2 

37 

9 

31 

7 

6 

22 

9 

2 

56 

9 

36 

6 

51 

21 

10 

3 

16 

9 

41 

6 

35 

20 

11 

3 

34 

9 

45 

6 

19 

19 

12 

3 

53 

9 

49 

6 

2 

18 

IS 

4 

11 

9 

51 

5 

45 

17 

14 

4 

29 

9 

53 

5 

27 

16 

15 

4 

47 

9 

54 

5 

9 

15 

16 

5 

4 

9 

55 

4 

50 

14 

17 

5 

21 

9 

55 

4 

31 

IS 

18 

5 

38 

9 

54 

k 

13 

12 

19 

5 

54 

9 

53 

3 

52 

11 

20 

6 

10 

9 

50 

3 

32 

10 

21 

6 

26 

9 

47 

3 

12 

9 

22 

6 

41 

9 

43 

2 

51 

8 

23 

6 

35 

9 

38 

2 

SO 

7 

24 

7 

9 

9 

S3 

2 

9 

6 

25 

7 

23 

9 

27 

1 

48 

5 

26 

7 

36 

9 

20 

1 

27 

4 

27 

7 

49 

9 

IS 

1 

5 

3 

28 

8 

1 

9 

5 

0 

43 

2 

1 29 

8 

IS 

9 

56 

0 

22 

1 

\ SO 

8 

24 

8 

46 

0 

0 

0 

12 au 


a 

95 

til 

f4€tu 

' X 

AW 

V5 


jSun slower 

than the 

clock in 





















the terrestrial globe. 221 

of degrees on the ecliptic exceed those on the equator, 
the sun is faster than the clock ; but if the number of 
degrees on the equator exceed those on the ecliptic, the 
sun is slower than the clock. 

Examples. 1. What is the equation of time on the 
irih of July ? 

Answer. The degrees on the equator exceed the degrees on the 
ecliptic by two; hence, the sun is eight minutes slower than the clock. 

2. On what four days of the year is the equation of 
time nothing ? 

3. What is the equation of time dependent on the 
obliquity ot the ecliptic on the 27th of October ? 

4. When the sun is 18° of Aries, what is the equa¬ 
tion of time ? 


PROBLEM XLI. 

To find the siin^s meridian altitude at any time of the: 
year at any given place. 

Rule. Find the sun’s declination, and elevate the 
pole to that declination; bring the given place to the 
brass meridian, and count the number of degrees on the 
brass meridian (the nearest way) to the horizon; these 
degrees will show the sun’s meridian altitude.f 

Note. The Sufi's altitude may be found at any particular hour, in tkt 
following manner. 

Find the sun’s declination, and elevate the pole to tha| declination ; 
bring the given place to the brass meridian and set the index to 12 ; 
then, if the given time be before noon, turn the globe Westward as many 
hours as the time wants of noon ; if the given time be past noon, turm 
the globe eastward as many hours as the time is past noon. Keep the 
globe fixed in this position, and screw the quadrant of altitude on the 
brass meridian over the sun’s declination; bring the graduated edge of 
the quadrant to coincide with the given place, and the number of de- 
^ees between that place and the horizon will show the sun’s altitude. 

OR, 

Elevate the pole so many degrees above the horizon 
as are equal to the latitude of the place ; find the sun’s 


* The learner will observe, that the equation of time here determin¬ 
ed is not the t- ue equation, as noted on the 7th circle on the horizon of 
Bardin’s globes; the equation of time there given cannot be determin¬ 
ed by the globe, 
t See Problem XXI. 



222 


PROBLEMS PERFORMED BY 


place in the ecliptic, and bring it to that part of the 
brass meridian which is numbered from the equator to¬ 
wards the poles ; count the number of degrees contain¬ 
ed on the brass meridian between the sun’s place and 
the horizon, and they will show the altitude.* 

To find the sun’s altitude at any hour, see Problem XLIV. 

OR, BY THE ANALBMMA. 

Elevate the pole so many degrees above the horizon 
as are equal to the latitude of the place ; find the day of 
the month on the analemma, and bring it to that part of 
the brass meridian which is numbered from the equator 
towards the poles ; count the number of degrees contain¬ 
ed on the brass meridian between the given day of the 
month and the horizon, and they will show the altitude. 

To find the sun’s altitude at any hour, see Problem XLIV. 

Examples. 1. What is the sun’s meridian altitude at 
London on the 21 st of June ? 

Answer. 62 degrees. 

2. What is the sun’s meridian altitude at London on 
the 21st of March ? 

3. What is the sun’s least meridian altitude at Lon¬ 
don ? 

4. What is the sun’s greatest meridian altitude at 
Cape Horn ? 

5. What is the sun’s meridian altitude at Madras on 
the 20th of June ? 

6. What is the sun’s meridian altitude at Bencooleu 
on the 15th of January ? 

EXAMPLES TO THE NOTE. 

1. What is the sun’s altitude at Madrid on the 24th 
of August, at 11 o’clock in the morning 


* See Problem XXII. • 

t This example is taken from a prospectus, announcing the publican 
tion of New Globes, to be executed by Mr. Dudley Adams, and called 
the Newtonian Globes, wherein the author has treated the common 
globes with uncommon severity; he has however been rather unfortu¬ 
nate in the choice of his examples, which are designed to show “ the ab¬ 
surdities and ridiculous inconsistencies of the common globes ” He says, 
“ By working this problem on the common globes, we find with the 
greatest astonishment, that Madrid, where it is understood to be eleven 



THE TERRESTRIAL GLOBE. 


223 

Answer. The sim^s declination is 11^ degrees north, by elevating 
the north pole Hi degrees above the horizon, and turning the globe so 
that Madrid may be one hour westward of the meridian, the sun’s alti¬ 
tude will be found to be 51^ degrees. 

2. What is the sun’s altitude at London at 3 o’clock 
in the afternoon on the 25th of April ? 

3. What is the sun’s altitude at Rome on the 16th of 
January at 10 o’clock in the morning? 

4. Required the sun’s altitude at Buenos Ayres on 
the 21st of December at 2 o’clock in the afternoon. 

PROBLEM XLII. 

When it is midnight at any place in the temperate or 

torrid zones, to find the sun^s altitude at anyplace (on 

the same meridian) in the north frigid zone, where the 

sun does not descend below the horizon. 

Rule. Find the sun’s declination for the given day, 
and elevate the pole to that declination; bring the place 
(in the frigid zone) to that part of the brass meridian 
which is numbered from the north pole towards the e- 
quator, and the number of degrees between it and the 
horizon will be the sun’s altitude. 

OR, 

Elevate the north pole so many degrees above the ho¬ 
rizon as are equal to the latitude of the place in the frig¬ 
id zone; bring the sun’s place in the ecliptic to the brass 
meridian, and set the index of the hour circle to twelve ; 
turn the globe on its axis till the index points to the 
other twelve; and the number of degrees between the 
sun’s place and the horizon, counted on the brass meri¬ 
dian towards that part of the horizon marked north, will 
be the sun’s altitude. 

Examples. 1. What is the sun’s altitude at the North 
Cape in Lapland, when it is midnight at Alexandria in 
Egypt on the 21st of June ? 


o’clock in the morning, is at that time in the dark, under the horizon ; 
and consequently, we hardly conceive how the inhabitants can see the 
sun take its altitude, and calculate the time to be eleven o’cloqk .”—Ex 
uno disce Omnes. 



224 


PROBLEMS PERFORMED BY 


Answer. 5 degrees. 

2. When it is midnight to the inhabitants of the island 
of Sicilj on the 22d of Maj, what is the sun’s altitude 
at the north of Spitzbergen, in latitude 80® north ? 

3. What is the sun’s altitude at the north east of Nova 
Zembla, when it is midnight at Tobolsk, on the 15th of 
July ? 

4. What is the sun’s altitude at the north of Baffin’s 
Bay, when it is midnight at Buenos Ayres, on the 28th 
of May ? 


PROBLEM XLIII. 

To find the sun^s amplitude at any place. 

Elevate the pole so many degrees above the horizon 
as are equal to the latitude of the given place ; find the 
sun’s place in the ecliptic, and bring it to the eastern 
semi-circle of the horizon; the number of degrees from 
the sun’s place to the east point of the horizon will be the 
rising amplitude: bring the sun’s place to the western 
semi-circle of the horizon, and the number of degrees 
from the sun’s place to the west point of the horizon will 
be the setting amplitude. 

OR, BY THE ANALEMMA. 

Elevate the pole so many degrees above the horizon 
as are equal to the latitude of the place; bring the day of 
the month on the analemma to the eastern semi-circle of 
the horizon; the number of degrees from the day of the 
month to the east point of the horizon will be the rising 
amplitude: bring the day of the month to the western 
semi-circle of the horizon, and the number of degrees 
from the day of the month to the west point of the hori¬ 
zon will be the setting amplitude. 

Examples. 1. What is the sun’s amplitude at Lon¬ 
don on the 21st of June ? 

Answer. 39® 48' to the n *rth of the east, and 39® 48' to the north 
of the west. 

2. On what point of the compass does the sun rise and 
set at London on the 17th of May ? 

3. On what point of the compass does the sun rise and 
^et at the Cape ot Good Hope on the 21st of December ? 


THE TERRESTRIAL GLOBE. 225 

4. On what point of the compass does the sun rise and 
set on the 21st of March ? 

5. On what point of the compass does the sun rise and 
set at Washington on the 21st of October ? 

6. On what point of the compass does the sun rise 
and set at Petersburg on the 18th of December ? 

PROBLEM XLIV. 

To find the sun^s azimuth and his altitude at any 
plac€y the day and hour being given* 

« 

Rule* Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the place, and 
screw the quadrant of altitude on the brass meridian, 
over that latitude; find the sun’s place in the ecliptic, 
bring it to the brass meridian, and set the index of the 
hour circle to twelve ; then, if the given time be before 
noon, turn the globe eastward* as many hours as it wants 
of noon; but if the given time be past noon, turn the 
globe westward as many hours as it is past noon; bring 
the graduated edge of the quadrant of altitude to coin¬ 
cide with the sun’s place, then the number of degrees on 
the horizon, reckoned from the north or south point 
thereof to the graduated edge of the quadrant, will show 
the azimuth; and the number of degrees on the quad¬ 
rant, counting from the horizon to the sun’s place will be 
the sun’s altitude. 

OR, BY THE ANALEMMA. 

Elevate the pole so many degrees above the horizon 
as are equal to the latitude of the place, and screw the 
quadrant of altitude on the brass meridian, over that 
latitude; bring the middle of the analemma to the brass 
meridian, and set the index of the hour circle to twelve; 
then, if the given time be before noon, turn the globe 


* Whenever the pole is elevated for the latitude of the place, the 
proper motion of the globe is from east to west, and the sun is on the 
east side of the brass meridian in the morning, and on the west side in 
the afternoon ; but, when the pole is elevated for the sun’s declination, 
the motion is from west to east, aud the place is on the west side of the 
meridian in the morning, and on the east side in the afternoon. 

31 







226 PROBLEMS PERFORMED BY ;; 

eastward on its axis as many hours as it wants of noon ; 
but, if the given lime be past noon, turn the globe west¬ 
ward as many hours as it is past noon; bring the gradu¬ 
ated edge of the quadrant of altitude to coincide with 
the day of the month on the ariaiemma, then the number 
of degrees on the horizon, reckoned trom the north or 
south point thereof to the graduated edge of the quad¬ 
rant, will show the azimuth ; and the number of degrees 
on the quadrant, counting from the horizon to the day 
of the month, will be the sun’s altitude. 

^ Examples. 1. What is the son’s altitude, and his 
azimuth from the north, at London, on the 1st of May, 
at ten o’clock in the morning ? 

Answer. The altitude is iT®, and the azimuth from the north 1S5°, 
or from the south 44°. 

2. W hat is the sun’s altitude and azimuth at Peters¬ 
burg, on the 13th of August, at half past five o’clock in 
the morning ? 

3. What is the sun’s azimuth and altitude at Antigua, 
on the 21st of June, at half past six in the morning, and 
at half past ten 

4. At Barbadoes on the 20lh of May, when the sun’s 
declination is 20 degrees north, required the time of the 
sun’s appearing on the same azimuth, twice in the fore¬ 
noon and twice in the afternoon ? 

5. On the 13th of August at half past eight o’clock in 
the morning, at sea in latitude 57° N. the observed azi¬ 
muth of the sun was S. 40° 14' E. what was the the sun’s 
altitude, his true azimuth, and the variation of the com¬ 
pass? 

6. On the 14th of January, in latitude 33° 52' S. at 
half past three o’clock in the afternoon, the sun’s mag¬ 
netic azimuth was observed to be N. 63° 51' W.; what 
was the true azimuth, the variation of the compass, and 
the sun’s altitude ? 


* At all places in the torrid zone, whenever,the declination of the 
sun exceeds the latitude of the place, and both are of the same name, 
the sun will appear twice in the forenoon and twice in the afternoon, 
on the same point of the compass and will cause the shadow of an azi¬ 
muth dial to go back several degrees. In this example, the sun’s, azi¬ 
muth at the hours given above, will be 69° from the north towards the 
east; and at half past eight o’clock, the sun will appear to have the 
same azimuth for some time. 





THE TERRESTRIAL GLOBE. 


227 


PBOBLEM XLV. 

The latitude of the place, day of the month, and the 
sun^s altitude being given, to find the stints azimuth 
and the hour of the day,^ 

Rule* Elevate the pole as many,degrees above the 
horizon as are equal to the latitude of the place, and 
screw the quadrant of altitude on the brass meridian, 
over that latitude; bring the sun’s place in the ecliptic 
to the brass meridian, and set the index of the hour cir¬ 
cle to twelve; turn the globe on its axis till the sun’s 
place in the ecliptic coincides with the given degree of 
altitude on the quadrant; the hours passed over by the 
index of the hour circle will show the time from noon, and 
the azimuth will be found on the horizon, as in the pre¬ 
ceding problem. 

OR, BY THE ANALEMMA. 

Elevate the pole to the latitude of the place, and 
screw the quadrant of altitude over that latitude; bring 
the middle of the analerama to the brass meridian, and 
set the index of the hour circle to twelve; move the 
globe and the quadrant till the day of the month coin¬ 
cides with the given altitude, the hours passed over by 
the index will show the time from noon, and the azimuth 
will be found in the horizon as before. 

Examples. 1. At what hour of the day on the 21st 
of March is the sun’s altitude 221° at London, and what 
is his azimuth ? The observation being made in the af¬ 
ternoon. 


* This problem is only a variation of the preceding ; for, by the na¬ 
ture of spherical trignometry, any three of the following quantities, 
viz. the latitude of the place, the sun’s declination, altitude, azimuth, 
or time of the day, being given, the rest may be found, admitting of 
several variations. A large collection of astronomical problems may 
be found in Keith’s Trigonometry, second edition, page 246, &c. Tb^se 
problems are useful exercises on the globes. 



228 


PROBLEMS PERFORMED BY 


Answer. The time from noon will be found to be 3 hours SO min¬ 
utes, and the azimuth 59° 1' from the south towards the west. Had 
the observation been made before noon, the time from noon would have 
been 3^ hours, viz. it would have been 30 minutes past eight in the 
morning, and the azimuth would have been 59° 1' from the south to- 
tvards the east.* 

2. Al what hour on the 9th of March is the sun’s al¬ 
titude 25® at London, and what is his azimuth ? The 
observation being; made in the forenoon. 

3. At what hour on the 18th ot May is the sun’s alti¬ 
tude 30° a( Lisbon, and what is his azimulh? The ob¬ 
servation being made in the afternoon 

4. Walking along the side of Queen-square in Lon¬ 
don, on the 5th of August in the forenoon, 1 observed 
the shadows of the iron-rails to be exactly the same 
length as the rails themselves ; pray what o’clock was 
it ? and on what point of the compass did the shadows 
of the rails fall ? 


PROBLEM XLVI. 


Given the lat itude of the place, and the day of the months 
to find at what place the sun is due east or west. 

Rule. Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the place, 6nd the 
sun’s place in the ecliptic, bring it to the brass meri¬ 
dian, and set the index of the hour circle to twelve ; 
screw the quadrant of altitude on the brass meridian, 
over the given latitude, and move the lower end of it to 
the east point of the horizon ; hold the quadrant in this 
position ; and move the globe on its axis fill the sun’s 
place comes to the graduated edge of the quadrant; the 
hours passed over by the index from twelve will be the 
time from noon when the sun is due east,f and at the 
same time from noon he will be due west. 


♦ The learner will observe, that the sun has the same altitude at 
equal distances from noon ; hence, it is necessary to say whether the ob¬ 
servation be made before or after noon, otherwise the problem admits 
of two answers. 

t If the latitude be north, and the sunN declination be south, he will 
be due east and west when he is below the horizon ; and the same thing 
will happen if the latitude be south when the declination is north. 



THE TERRESTRIAL GLOBE. 
OR, BY THE ANALEMMA. 


229 


This is exactly the same as above, only, instead of 
bringing the sun’s place lo the meridian, you bring the 
analemma there, and, instead of bringing the sun’s place 
to the graduated edge of the quadrant, (he day of the 
month on the analemma must be brought to it. 

Examples. 1. At what hour will the sun be due east 
at London on the 19th of May? at what hour will he be 
due west ? and what will his altitude be at these 
times ? 

Answer The time from 12, when the sun is due east, is i hours 54 
minutes hence, the sun is due east at 6 minutes past seven o’clock in 
the morning, and due w^est at 54 minutes past four in the afternoon ; the 
sun’s altitude may be found at the same time, as in Problem XLIV. 
In this example it is 25« 26'. 

2. At what hours will the sun be due east and west at 
London on the 21st of June, and on the 21st of Decem¬ 
ber? and what will be his altitude above the horizon on 
the 21st of June ? 

3. Find at what hours the sun will be due east and 
west, not only at London, but at every place on the sur¬ 
face of the globe, on the 21st of March and on the 23d 
of September. 

4. At what hours is the sun due east and west at 
Buenos Ayres on the 21st of December ? 

PROBLEM XLVII. 

Given the siin^s meridian altitude, and the day of the 
month, to find the latitude of the place. 

Rule. Find the sun’s place in the ecliptic, and bring 
it to that part of the brass meridian which is numbered 
from the equator towards the poles ; then, if the sun was 
south* of the observer when the altitude was taken, 


Examples exercising these cases are useless; however, they are easily 
solved, if we consider that, when the sun is due east below the horizon 
at any time, the opposite point of the ecliptic will be due west above 
the horizon ; therefore, instead of bringing the lower edge of the quad¬ 
rant to the east of the horizon, bring it to the west, and, instead of 
using the sun’s place, make use of a point in the ecliptic diametiically 
opposite. 

* It is necessary to state whether the sun be to the north or south of 
the; observer at noon, otherwise the problem is unlimited. 



230 


PROBLEMS PERFORMED BY 


count the number of degrees from the sun’s place on the 
brass meridian towards the south point of the horizon, 
and mark where the reckoning ends; bring this mark to 
coincide with the south point of Ihe horizon, and the ele¬ 
vation of the north pole will show the latitude. If the 
sun was north of the observer when the altitude was ta¬ 
ken, the degrees must be counted in a similar manner, 
from the sun’s place towards the north point of the hori¬ 
zon, and the elevation of the south pole will show the 
latitude. 

OR, WITHOUT 4 GLOBE. 

Subtract the sun’s altitude from ninety degrees, the 
remainder is the zenith distance. If the sun be south 
when his altitude is taken, call the zenith distance 
north ; but, if north, call it south ; find the sun’s declina¬ 
tion in an ephemeris* ora table of the sun’s declination, 
and mark whether it be north or south; then, if the zen¬ 
ith distance and declination have the same name, their 
sum is the latitude ; but if they have contrary names, 
their ditFerence is the latitude, and it is always of the 
same name with the greater of the two quantities. 

Examples. 1. On the 10th of May 1811,1 observed 
the sun’s meridian altitude to be 50°, and it was south of 
me at that time; required the latitude of the place. 

Answer. 57° 27' north. 


By calculation. 

90° 0 

50 0 S. sun’s altitude at noon. 


40 0 N. the zenith distance. 

17 27 N. the sun’s declination 10th May, 1811, 

57 27 N. the latitude sought. 

*2. On the 10th of May 1811, the sun’s meridian alti¬ 
tude was observed to be 50”, and it was north of the 
observer at that time; required the latitude of the place. 
Answer. 23® 33' south. 


* The most convenient is the Nautical Almanac, or White’s Ephero* 
eris; see the note page 38. 







TUB TERRESTRI AL GLOBE. , 231 

By calculation. > 

90® 0 

50 ON. the sun’s altitiule at noon. 

40 0 S. the zenith distance. 

17 27 N. the sun’s declination 10th May 1811. 

22 S3 S. the latitude sought. 

3. On the 5th of August 1811, the sun’s meridian al¬ 
titude was observed to be 74® 30' north of the obser¬ 
ver ; what was the latitude ? 

4. On the 19th of November 1811, the sun’s meridian 
altitude was observed to be 40° south of the observer ; 
what was the latitude ? 

5. At a certain place where the clocks are 2 hours 
faster than at London, the sun’s meridian altitude was 
observed to be 30 degrees to the south of the observer 
on the 21st of March ; required the place. ’ 

6. At a place where the clocks are five hours slower 
than at London, the sun’s meridian altitude was observed 
to be 60° to the south of the observer on the 16th of 
April, 1811 : required the place. 

PROBLEM XLVIII. 

The length of the longest day at any place, not wilhm 

the polar circles being given, to find the latitude of 

that place. 

Rule. Bring the first point of Cancer or Capricorn to 
the brass meridian (according as the place is on the 
north or south side of the equator,) and set the index of 
the hour circle to twelve ; turn the globe westward on its 
axis till the index of the hour circle has passed over as 
many hours as are equal to half the length of the day ; 
elevate or depress the pole till the sun’s place (viz. Can¬ 
cer or Capricorn) comes to the horizon ; then, the eleva¬ 
tion of the pole will show the latitude. 

Note. This problem wiH answer for any day in the year, as well as 
the longest day, by btinging the sun’s place to the brass meridian and 
proceeding as above. 

Or, Bring the middle of the analemraa to the brass meridian, and set 
the index of the hour circle to 12; turn the globe westward on its axis 
till the index has passed over as many hours as are equal to half the 
length of the day; elevate or depress the pole till the day of the month 
coincides with the horizon, then the elevation of the pole will show the 
latitude. 




232 


PROBLEMS PERFORMED BY 


Examples. 1. In what degree of north latitude, and 
at what places is the length of the longest day 16|^ 
hours ? 

Answer. In latitude 52°, and all places situated on, or near that 
parallel of latitude, have the same length of day. 

2. In what degree of south latitude, and at what pla¬ 
ces is the longest day 14 hours ? 

3. In what degree of north latitude is the length of 
the longest day three times the length of the shortest 
night ? 

4. There is a town in Norway where the longest day 
is five times the length of the shortest night ; pray what 
is the name of the town ? 

5. In what latitude north does the sun set at seven 
o’clock on the 5th of April ? 

6. In what latitude south does the sun rise at five 
o’clock on the 25th of November I 

7. In what latitude north is the 20th of May 16 hours 
long ? 

8. In what latitude north is the night of the 15th of 
August 10 hours long ? 

PROBLEM XLIX. 

The latitude of a place, and the day of the month being 
given, to find how much the sun^s declination must 
increase or decrease towards the elevated pole, to 
make the day an hour longer or shorter than the giv¬ 
en day. 

Rule. Find the sun’s declination for the given day, 
and elevate the pole to that declination ; bring the given 
place to the brass meridian, and set the index of the 
hour circle to twelve ; turn the globe eastward on its ax¬ 
is till the given place comes to the horizon, and observe 
the hours passed over by the index : then, if the days be 
increasing, continue the motion of the globe eastward 
till the index has passed over another half hour, and 
raise the pole till the place comes again into the horizon, 
the elevation of the pole will show the sun’s declination 
when the day is an hour longer than the given day : but, 
if the days be decreasing, turn the globe westward till 
the index has passed over half an hour, and depress the 
pole till the place comes a second time into the horizon, 


THE TERRESTRIAL GLOBE. 


233 


the last elevation of the pole will show the sun’s decli¬ 
nation when the day is an hour shorter than the given 
day. 


OR, 

Elevate the pole to the latitude of the place, find the 
sun’s place in the ecliptic, bring it to the brass meridian, 
and set the index of the hour circle to twelve ; turn the 
globe westward on its axis till the sun’s place comes to 
the horizon, and observe the hours passed over by the 
index; then, if the days be increasing, continue the mo¬ 
tion of the globe westward till the index has passed 
over another half hour, and observe what point of the 
ecliptic is cut by the horizon ; that point will show the 
sun’s place when the day is an hour longer than the giv¬ 
en day, whence the declination is readily found : but, if 
the days be decreasing, turn the globe eastward till the 
index has passed over half an hour, and observe what 
point of the ecliptic is cut by the horizon ; that point 
will show the sun’s place when the day is an hour short¬ 
er than the given day. 

OR, BY THE ANALEMMA. 

Proceed exactly the same as above, only, instead of 
bringing the sun’s place to the brass meridian, bring the 
analemma there, and, instead of the sun’s place, use the 
day of the month on the analemma. 

Examples, 1. How much must the sun’s declination 
vary, that the day at London may be increased one hour 
from the 24th of February ? 

Answer. On the 24th of February the sun’s declination is 9® 38'^ 
south, and the sun sets at a quarter past five : when the sun sets at 
three quarters past five, his declination will be found to be about 
south, answering to the 10th of March; hence, the declination has de¬ 
creased 5° 2y, and the days have increased 1 hour in 14 days. 

2. How much must the sun’s declination vary, that 
the day at London may decrease one hour in length from 
the 26th of July ? 

Answer The sun’s declination on the 26th of July is 19® 38' north, 
and the sun sets at 49 min. past seven ; when the sun sets at 19 min. 
past seven, his declination will be found to be 14° 43' north, answering 
to the ISth of August: hence, the declination has decreased 5® 55 , and 
the days have decreased one hour in 18 days. 

32 


234 


FROBLEIMS PERFORMED BY 


3. How much must the sun’s declination varj, from 
the 5lh of April, that the day at Petersburg may in¬ 
crease one hour ? 

4. How much must the sun’s declination vary, from 
ihe 4th of October, that the day at Stockholm may de¬ 
crease one hour. 


PROBLEM L. 

To find the smi’s right ascension, oblique ascension^ 
oblique deseension, ascensional difference, and time 
of rising and setting at anyplace* 

Rule* Find the sun’s place in the ecliptic, and bring 
it to that part of the brass meridian which is numbered 
from the equator towards the poles the degree on the 
equator cut by the graduated edge of the brass meridi¬ 
an, reckoning from the point Aries eastward, wilfbe the 
sun’s right ascension* 

Elevate the pole so many degrees above the horizon 
as are eq^ial to the latitude of the place, bring the sun’s 
place in the ecliptic to the eastern part of the horizon,f 
and the degree on the equator cut by the horizon, reck¬ 
oning from the point Aries eastward, will be the sun’s 
oblique ascension. Bring the sun’s place in the eclip¬ 
tic to the western part of the horizon, J and the degree 
on the equator cut by the horizon, reckoning from the 
point Aries eastward, will be the sun’s oblique descen- 
sion. 

Find the difference between the sun’s right and ob¬ 
lique ascension ; or, which is the same thing, the differ¬ 
ence between the right ascension, and oblique descen- 
sion, and turn this difference into time by multiplying by 
4;§ then, if the sun’s declination and the latitude of 
the place be both of the same name, viz. both north or 
both south, the sun rises before six, and sets after six, by 


* The degree on the meridian above the sun’s place is the sun’s de¬ 
clination. See Prob. XX. 

t The rising amplitude may be seen at the same time. See Problem. 
XLIII. 


t The setting amplitude may here be seen. Vide Prob. XLIIL 
J See Problem XVIII. 





THE TERRESTRIAL GLOBE. 


235 


a space of time equal to the ascensional difference ; but, 
if the sun’s declination and the latitude be of contrary- 
names, viz. the one north, and the other south, the sun 
rises after six, and sets before six. 

Examples. 1. Required the sun’s right ascension, 
oblique ascension, oblique descension, ascensional differ¬ 
ence, and time of rising and setting at London, on the 
15th of April, 

Answer. The right ascension is 23® SO', the oblique ascension is 9® 
45', the ascensional difference (23® SO'—9® 45'==) IS® 45', or 55 min¬ 
utes of time; consequently, the sun rises 55 minutes before 6, or 5 min. 
past 5, and sets 55 min. past 6. The oblique descension is 37® 15' ; 
consequently, the descensional difference is (37® 15'— 23® SO's==) 13® 45' 
the same as the ascensional difference. 

2. Wliat are the sun’s right ascension, oblique ascen¬ 
sion, and oblique descension, on the 27 th of September 
at London ? What is the ascensional difference, and at 
what time does the sun rise and set ? 

3. What are the sun’s right ascension, declination, 
oblique ascension, rising amplitude, oblique descension, 
and setting amplitude, at London, on the 1st of May ? 
What is the ascensional difference, and at what time 
does the sun rise and set ? 

4. What are the sun’s right ascension, declination, 
oblique ascension, rising amplitude, oblique descension, 
and setting amplitude at Petersburg, on the 21 st of June ? 
What is the ascensional difference, and at what time does 
the sun rise and set ? 

5. What are the sun’s right ascension, declination, 
oblique ascension, rising amplitude, oblique descension, 
and setting amplitude, at Alexandria, on the 21st of De¬ 
cember ? What is the ascensional difference, and at what; 
time does the sun rise and set ? 

PROBLEM LI. 

Given the day of the months and the sun's ampliiudey to 
find the latitude of the place of observation* 

Rule. Find the sun’s place in the ecliptic, and bring 
it to the eastern or western part of the horizon (accor¬ 
ding as the eastern or western amplitude is given,) ele¬ 
vate or depress the pole till the sun’s place coincides 


236 


PROBLEMS PERFORMED BY 


with the given amplitude on the horizon, then the eleva- 
tion of the pole will show the latitude. 


OR THUS, 

Elevate the north pole to the complement* of the am¬ 
plitude, and screw the quadrant of altitude upon the 
brass meridian over the same degree ; bring the equi¬ 
noctial point Aries to the brass meridian, and move the 
quadrant of altitude till the sun’s declination for the giv¬ 
en daj (counted on the quadrant) coincides with the 
equator ; the number of degrees between the point Aries 
and the graduated edge of the quadrant will be the lati¬ 
tude sought. 

Examples, 1. The sun’s amplitude was observed 
to be 39® 48' from the east towards the north, on the 21st 
of June ; required the latitude of the place. 

Answer. 51® 32' north.t 

2. The sun’s amplitude was observed to be 15® 30' 
from the east towards the north, at the same time his de¬ 
clination was 15® 30' ; required the latitude. 

Answer. The latitude was nothing. 

3. On the 29th of May, when the sun’s declination 
was 21° 30' north, his rising amplitude was known to be 
22° northward of the east ; required the latitude. 

Answer. 12® north. 

4. When the sun’s declination was 2° north, his rising 
amplitude was 4° north of the east; required the lati¬ 
tude. 

Answer. 60® north. 


♦ The complement of the amplitude is found by subtracting the am¬ 
plitude from 90®. This rule is exactly the same as abo\ne ; for it is 
formed from a right-angled spherical triangle, the base being the com¬ 
plement of the amplitude, the perpendicular, the latitude of the place, 
and the hypothenuse the complement of the sun’s declination, 
t See Keith’s Trigonometry, second edition, page 253. 



THE TERRESTRIAL GLOBE. 


237 


PROBLEM LII. 

Given two observed altitudes of the sim, the time 
elapsed between thenii and the sun^s declination, to 
find the latitude-^ 

Rule. Find the sun’s declination, either by the globe 
or an epheineris ; take the number of degrees contained 
therein from the equator, with a pair of compasses, and 
apply the same number of degrees upon the meridian 
passing through Libra f from the equator northward or 
southward, and mark where they extend to; turn the 
elapsed time into degrees, J and count those degrees 
upon the equator from the meridian passing through 
Libra ; bring that point of the equator where the reck¬ 
oning ends to the graduated edge of the brass meridian, 
and set off the sun’s declination from that point along 
the edge of the meridian, the same way as before ; then 
take the complement of the first altitude from the equa¬ 
tor in your compasses, and, with one foot in the sun’s 
declination, and a fine pencil in the other foot, describe 
an arc; take the complement of the second altitude in a 
similar manner from the equator, and, with one foot of 
the compasses fixed in the second point of the sun’s de¬ 
clination, cross the former arc ; the point of intersec¬ 
tion brought to that part of the brass meridian which is 
numbered from the equator towards the poles, will stand 
under the degree of latitude sought. 

Examples. 1. Suppose on the 4th of June, 1813, in 
north latitude, the sun’s altitude, at 29 minutes past 10 
in the forenoon, to be 65° 24', and at 31 minutes past 
12, 74° 8'; required the latitude. 


* Dr Wilson, in his Dissertation on the Rise and Progress of Navi¬ 
gation, prefixed to Robertson’s Treatise, says, this problem was first 
solved by the globe by Mr. Robert Hues, and published in 1594; and 
Dr. Mackay, in page 158 of his Complete Navigator, mentions the 
same circumstance. I have not been able to procure this book, nor 
have I ever seen a solution to the problem by the globe. 

t Any meridian will answer the purpose as well as that which pass¬ 
es through Libra; on Adams’ globes this meridian is divided like th^ 
brass meridian. 

t See the method of turning time into degrees, Prob. XTX. 



23& 


PROBLEMS PERFORMED BY 


Answer. Thje sun»s declination is 22° 27' north, the elapsed time two 
hours two min. answering to 30° SO'; the complement of the first alti¬ 
tude 24° 36', the complement of the second altitude 15° 52', and the 
latitude sought, 36° 57' north. 

2. Given the sun’s declination 19° 39' north, his al¬ 
titude in the forenoon 38° 19', and, at the end of one, 
hour and a half, the same morning the altitude was 50° 
25' ; required the latitude of the place, supposing it to 
be north. 

Answer. 51° 32' north.* 

3. When the sun’s declination was 22° 40' north, his 
altitude at 10 h. 54 m. in the forenoon was 53° 29', and 
at 1 h. 17 m. in the afternoon it was 52° 48'; required 
the latitude of the place of observation, supposing it to 
be north. 

Answer. 57° 8' north. 

4. In north latitude, when the sun’s declination was 
22° 23' south, being on the 5th of December, the sun’s 
altitude in the afternoon was observed to be 14° 46', and 
after 1 h. 22 m. had elapsed, his altitude was 8° 27' ; 
required the latitude. 

Answer. 50° 34' north. 

PROBLEM LIII. 

The day and hour being given when a solar eclipse wiU 
happen, to find where it will he visible. 

Rale. Find the sun’s declination, and elevate the 
pole agreeably to that declination; bring the place at 
which the hour is given, to that part of the brass meri¬ 
dian which is numbered from the equator towards the 
poles, and' set the index of the hour circle to twelve ; 
then, if the given time be before noon, turn the globe 
westward till the index has passed over as many hours 
as the given time wants of noon; if the time be past noon, 
turn the globe eastward as many hours as it is past noon, 
and exactly under the degree of the sun’s declination on 
the brass meridian, you will find the place on the globe 
where the sun will be vertically eclipsed: at all places 


♦ A peat variety of examples, accurately calculated by a general 
rule, without an assumed latitude, may be seen in Keith’s Trigonome* 
try, second -edition, page 292, &c. 



THE TERRESTRIAL GLOBE. 239 

within 70 degrees of this place, the eclipse may* be 
visible, especially if it be a total eclipse. 

Example. On the 11th of February, 1804, at 27 min. 
past ten o’clock in the morning at London, there was an 
eclipse of the sun ; where was it visible, supposing the 
moon’s penumbral shadow to extend northward 70 de¬ 
grees from the place where the sun was vertically eclip¬ 
sed ? 

Answer. London, &:c. For more examples consult the Table of 
Eclipses, following the next problem. 


PROBLEM LIV. 

The day and hour being given when a lunar eclipse 
will happen, to find where it w ill be visible. 

Rule. Find the sun’s declination for the given day, 
and note whether it be north or south ; if it be north, 
elevate the south pole so many degrees above the hori¬ 
zon as are equal to the declination; if it be south, elevate 
the north pole in a similar manner: bring the place at 
which the hour is given to that part of the brass meri¬ 
dian which is numbered from the equator towards the 
poles, and set the index of the hour circle to twelve ; 
then, if the given time be before noon, turn the globe 
westward as many hours as it wants of noon ; if after 
noon, turn the globe eastward as many hours as it is past 
noon; the place exactly under the degree of the sun’s 
declination will be the antipodes of the place where the 
moon is vertically eclipsed. Set the index of the hour 
circle again to twelve, and turn the globe on its axis till 
the index has passed over twelve hours; then to all pla¬ 
ces above the horizon the eclipse will be visible; to those 
places along the western edge of the horizon the moon 
will rise eclipsed; to those along the eastern edge she 
will set eclipsed ; and to that place immediately under 


* When the moon is exactly in the node, and when the axes of the 
moon’s shadow and penumbra pass through the centre of the earth, the 
breadth of the earth’s surface under the penumbral shadow is 70° 20'; 
but the breadth of this shadow is variable; and, if it be not accurately 
determined by calculation, it is impossible to tell by the globe to what 
extent an eclipse of the sun will be visible. 



210 


PROBLEMS PERFORMED BY 


the sun’s declination the moon will be rerlically eclip¬ 
sed. 

* Example, On the 26th of January; 1804, at 58 min. 
past seven in the afternoon at London, there was an 
eclipse of the moon; where was it visible? 

Answer. It was visible to the whole of Europe, Africa, and the con¬ 
tinent of Asia. For more examples, see the following Table of Eclip¬ 
ses. 

Note. The substance of the following Table of Eclipses was extract¬ 
ed from Dr. Hutton’s translation of Montucla’s edition of Ozanam’s 
Mathematical and Physical Recreations, published by Mr. Kearsley in 
fleet-street. These eclipses were originally calculated by M. Pingr^, 
a member of the Academy of Sciences, and published in UArt des veri¬ 
fier les Dates. In classing these tables, the arrangement of Mr. Fergu¬ 
son has been followed ; see page 267 of his Astronomy, where a cata¬ 
logue of the visible eclipses is given from 1700 to LsOO, taken from UArt 
des verifier les Dates. It may be necessary to inform the learner, that 
the times of these eclipses, as calculated by M Pingr^, are not perfect¬ 
ly accurate, and were only designed to show nearly the time when an 
eclipse may be expected to happen. The limits where these eclipses arc 
visible are generally from the tropic of Cancer in Africa, to the north¬ 
ern extremity of Lapland, and from the 5th degree of north latitude in 
Asia, to the north polar circle ; though some few of them are visible be¬ 
yond the pole. In longitude, the limits are the 5th and 155th meri¬ 
dians, supposing the 20th to pass through Paris ; hence, it appears that 
they are calculated for the meridian of Ferro; which will make their 
limits from London to be from 12® 46' west long, to 137® 14' east. M. 
Pingri says, that an eclipse of the sun is visible from 32® to 64® north, 
and as far south of the place where it is central. In the following table 
the moon is represented by M, the sun by S, t stands for total, p for 
partial, M for morning, and A for afternoon; the rest is obvious. 


THE TERRESTRIAL GLOBE. 


341 


1812 


1813 


1814 


1815 


1816 


1817 


1818 


1811 M 

-M 

M 
M 
S 
M 
M 
S 

s 

M 
M 
S 
M 
M 
S 
M 
S 
M 
S 
M 
S 
M 
M 
S 
S 
M 
M 
S 
M 
S 
M 
M 
M 
S 

s 

M 
M 
S 
M 
S 
M 


1819 


1820 


1821 

1822 


1823 


1824 


1825 


Months 

and 

Days. 


March 10 
Sep. 2 
Feb. 27 
4ug. 22 
Feb. 1 
Feb. 15 
Aug. 12 
Jan. 21 
July 17 
Dec. 26 
June 21 
July 7 
Dec. 16 
June 10 
ISov. 19 
pDec. 4 
May 16 
pMay 3 
Nov. 9 
April 21 
May 5 
pOct. 14 
April 10 
April 24 
Sep. 19 
Oct. 3 
March 29 
Sep. 7 
p Sep. 22 
March 4 
Feb. 6 
Aug. 3 
Jan. 26 
Feb. 11 
July 8 
July 23 
Jan. 16 
June 26 
July 11 
Dec. 20 
June 1 


Time. 


6iM 
11 A 
6M 
3 A 
9 M 
9 M 
3i M 
21 A 
7 M 
lliA 
61 A 
0 M 
HA 

II M 
101 M 

9 A 
7 M 
3iA 
21 M 
0^ M 
7i m 

6 M 

Ha 

Merid. 

1 A 
31 A 

7 A 

2 A 
7 M 
6 M 
51 M 
O^M 

3M 
61 M 
31 M 
9 M 

III A 
41 M 

11 M 
O^M 


1825 


1826 


1827 


1828 


1829 


1830 


1831 


1832 

1833 


1834 


1835 


1836 


1837 


1838 


1839 


1840 


S 

M 

M 

M 

S 

S 

M 

M 

S 

S 

M 

M 

S 

S 

M 

M 

M 

M 

S 

M 

M 

S 

M 

M 

M 

S 

M 

S 

M 

S 

M 

M 

S 

M 

M 

M 

S 

S 

M 

S 

M 


Months 

and (Time. 
Days. 


June 16 
Nov. 25 
May 21 
Nov. 14 
Nov. 29 
April 26 
May 11 
Nov. 3 
April 14 
Oct. 9 
March 20 
Sep. 13 
Sep. 28 
Feb. 23 
March 9 
Sep. 2 
Feb. 26 
Aug. 23 
July 27 
Jan. 6. 

P July 2 
July 17 
Dec. 26 
June 21 
Dec. 16 
May 27 
pJune 10 
Nov. 20 
May 1 
May 15 
Oct. 24 
April 20 
May 4 
Oct. 13 
April 10 
Oct. 3 
March 15 
Sep. 7 
Feb. 17 
March 4 
Aug. 13 


Oi A 
4i A 
31 A 
4^ A 
IH M 
H M 
^ M 
5 A 
9f M 
Oi M 
2 A 
7 M 
21 M 
5 M 

2 A 
11 A 

5 A 
101 M 
21 A 

3 M 

1 M 
7 M 

10 A 
81 M 
51 M 
H A 

11 A 
11 M 

H M 
2i A 
n A 

9 A 
7i A 
Hi A 
2i M 

3 A 
2i A 

lOi A 

2 A 

4 M 
7i M 


.33 








































































242 


PROBLEMS PERFORMED BY 


Years. 


Mouths 

and 

Days. 

Time. 

Years. 


Months 1 
and 
Days. 

Time. 

1841 

M t 

Feb. 6 

2i 

■^2 

M 

1856 

S 

Sep. 29 

4 

M 


S 


Feb. 21 

1 1 

M 


M p 

Oct. 13 

iH 

A 


s 


July 18 

2 

A 

1857 

S 

Sep. 18 

6 

M 


M 

t 

Au^. 2 

10 

M 

1858 

M p 

Feb. 27 


A 

1842 

iVI 

p 

Jau. 26 

6 

A 


S 

March 15 

Oi 

A 


s 


July 8 

7 

M 


M p 

Aug. 24 


A 


M 

p 

July 22 

11 

M 

1859 

M t 

Feb. 17 

11 ' 

M 

1843 

M 

p 

June 12 

8 

M 


S 

July 29 

H 

A 


M 


1 7 

oi 

M 


lU t 

Aug. 13 

H 

A 


s 

P 

Dec. 21 


M 

1860 

ifl 1 

M p 

Feb. 7 


M 

1844 

M t 

May 31 

lU 

A 


S 

July 18 

2 

A 


M 

t 

Nov. 25 

0} 

M 


M p 

Aug. 1 


A 

1845 

S 


May 6 

lOi 

M 

1861’ 

S 

Jan. 11 

H 

M 


M 

t 

May 21 

H 

A 


s 

July 8 

2 

M 

M 



1 

M 


M n 

Dec. 17 

8i 

M 

1846S 

P 

April 25 


A 


nj u 

s 

Dec. 31 

2i A 

__ 

S 


Oct. 20 

H 

M 

1862 

M t 

June 12 

63 

4 

M 

1847 

M 

P 

March 31 


A 


M t 

Dec. 6 

8 

M 


S 


Sep. 24 

3 

A 


S 

Dec. 21 


M 


s 


Oct. 9 


M 

1863 

S 

May 17 

5 

A 

1848 

M 

t 

March 19 


A 


Mt 

June 2 

0 

M 

— 

iVl 

t 

Sep. 13 


M 


M p 

Nov. 25 

0 

M 


s 


Sep. 27 

10 

M 

1864 

S 

May 6 

03 

^4 

M 

1849 

s 


Feb 23 

n 

M 

1865 

M p 

April 11 

5 

M 


M 

P 

March 9 

1 

M 


M p 

Oct. 4 

11 

A 


M 

P 

Sep. 2 


A 


S 

Oct. 19 

5 

A 

1850 

S 


Feb. 12 


M 

1866 

S 

March 16 

10 

A 


s 


Aug. 7 

10 

A 


M t 

March 31 

5 

M 

1851 

M 

P 

Jan. 17 

5 

A 


M t 

Sep. 24 


A 


M 

P 

July 13 


M 


S 

Oct. 8 

H 

A 


S 


July 28 


A 

1867 

s 

March 6 

10 

M 

1852 

M 

t 

Jan. 7 


M 


M p 

March 20 

9 

M 


M 

t 

July 1 

3| 

A 


M p 

Sep. 14 

1 

M 


S 


Dec. 11 

4 

M 

1868 

S 

Feb. 23 

21 

A 


IVI 

P 

Dec. 26 

1 

A 


S 

Aug. 18 


M 

1853 

M 

P 

June 21 

6 

M 

1869 

M p 

Jan. 28 

4 

M 

1854 

M 

P 

May 12 

4 

A 


M p 

July 23 

2 

A 

— 

M 

P 

Nov. 4 

91 A 

— 

S 

Aug. 7 

10 

A 

1855 

M 

t 

May 2 


M 

1870 

M i 

Jan. 17 

3 

A 


S 


May 16 


M 


M t 

July 12 

11 

A 

— 

M t 

Oct. 25 

8 

M 

- : 

S 

Dec. 22 

Of 

A 

1856 

IM 

P 

April 20 


M 

1871 

M p 

Jan. 6 

H 

A 






























































THE TERRESTRIAL GLOBE. 


243 


i ^ 

P3 


Months 

and 

Days. 

Time. 

Years 


Mouths 

and 

Days. 

Time. 

1871 

S 


June 18 


M 

1885 

M p 

Sep. 24 


M 


M 

P 

July 2 

‘i 

A 

1886 

s 

Aug. 29 

4 

A 


S 


Dec. 12 

H 

M 

1887 

M p 

Feb. 8 


M 

1872 

M 

P 

May 22 

14 

A 


M p 

Aug. 3 

9 

A 


S 


June 6 

H 

M 


s 

Aug. 19 

6 

M 


M 

P 

Nov. 15 

5i 

M 

1888 

M t 

Jan. 28 

*4 

A 

1873 

M 

t 

May 12 

111 

M 


M t 

July 23 

6 

M 


S 


May 26 

H 

M 

1889 

M p 

Jao. 1 7 

4 

M 


M 

t 

Nov. 4 

H A 


M p 

July 12 

9 

A 

1874 

M 

P 

May 1 


A 


S 

Dec. 22 

1 

A 


S 


Oct. 10 

IH 

M 

1890 

M p 

June 23 

6 

M 


M 

P 

Oct. 25 

8 

M 


s 

June 17 

lO 

M 

187^ 

S 


Apiil 6 

7 

M 

— 

M p 

Nov. 26. 

2 

A 


S 


Sep. 29 


A 

1891 

M t 

May 23 

7 

A 

1876 

M 

P 

March 10 

6i 

M 


S 

June 6 

4i 

A 


M 

P 

Sep. 3 


A 


M t 

Nov. 16 

o| 

M 

1877 

M 

t 

Feb. 27 

4 

A 

1892 

M p 

May 11 

14 

A 

— 

S 


March 15 

3 

M 


M t 

Nov. 4 


A 

f 

S 


Aug. 9 

5 

M 

1893 

S 

April 16 

3 

A 


M t 

Aug. 23 

14 

A 

1894 

M p 

March 21 


A 

1878 

M 

P 

Feb. 17 

'4 

M 


S 

April 6 


M 


S 


July 29 

94 

A 


M p 

Sep. 15 

4| 

M 


M 

P 

Aug. 13 

Ok 

M 


S 

Sep. 29 

H 

M 

1879 

S 


Jao. 22 

Merid. 

1895 

M t 

March 11 

4 

M 

! 

s 


July 19 

9 

M 


S 

March 26 

lo 

M 


M 

P 

Dec. 28 


A 


3 

Aug. 20 


A 

1880 

S 


Jan. 11 

11 

A 


VI t 

Sep. 4 

6 

M 


M t 

June 22 

2 

A 

1896 

M p 

Feb. 28 

8 

A 


M t 

Dec. 16 

4 

A 


S 

Aug. 9 

4i 

M 


S 


Dec. 31 

2 

A 


M p 

Aug 23. 

7 

M 

1881 

S 


May 28 

0 

M 

1897 

No 

visible Eclipse 

. 


M t 

June 12 


M 

1898 

M p 

Jan. 8 

Oi 

M 


M 

P 

Dec. 5 

H 

A 


S 

Jan. 22 

8 

M 

1882 

S 


May 17 

8 

M 


M p 

July 3 


A 


S 


Nov. 11 

0 

M 


M t 

Dec. 27 

12 

A 

1883 

M 

P 

April 22 

Merid. 

1899 

S 

Jan. 11 

11 

A 


M 

P 

Oct. 16 


M 


s 

June 8 

7 

M 


S 


Oct. 31 


M 


M t 

June 23 


A 

1884 

S 


March 27 

a 

M 


M p 

Dec. 17 

4 

M 


M t 

April 10 

Merid. 

1900 

S 

May 28 


A 


M t 

Oct. 4 

101 

A 


M p 

June 13 

4 

M 


S 


Oct. 19 

1 

M' 

— 

S 

Nov. 22 

8 

M 

1885 

M 

P 

March 30 

5 

A; 

















































































244 


PROBLEMS PERFORMED BY 


A TABLE, 

POR FINDING THE MOON’s AGE. 

Add the number taken from this table 
to the day of the month ; the sum (re¬ 
jecting 30, if it exceed SO,) is the 
age. 

Moon’s Age* 

High 

Water. 


> 

rt 

s 

B 

eo 

•-5 







c 

Qi 

1 

U 


Days 

H. M. 

Year 

' 5 
s 

"S 

1 March. 

1 April. 

> 

a 

c 

s 

»-5 

”5 

i-s 

1 August. 

a 

) ^ 
p. 
<u 
c/. 

October. 

£ 

a> 

> 

o 

-Q 

£ 

0) 

u 

<u 

0 

1 

2 

3 

4 

5 

0 0 

0 36 

1 11 

1 46 

2 21 

Q i 

1805 

0 

2 

1 2 

3 

; 4 

t 5 

i 6 

8 

8 

10 

10 

1806 

1807 

11 

22 

13 

24- 

12 IS 

13 U 

14 

25 

15 

26 

16 

27 

17 

28 

19 

0 

19 

0 

21 

2 

21 

2 

6 

7 

8 

Q 

O 1 

3 44 

4 37 

5 40 

1808 

3 

5 

T7 

6 

7 

8 

9 

11 

11 

13 

13 

V 

10 

11 

12 

IS 

14 

15 

0 Oo 

8 14 

9 17 

10 9 

10 53 

11 S3 

1809 

14 

16 1 

5 16 

17 

18 

19 

20 

22 

22 

24 

24 

1810 

25 

27 2 

<6127 

28 

29 

0 

1 

3 

3 

5 

5 

1811 

6 

8 

7 

Q 

10 

11 

12 

14 

14 

16 

16 

X-4r O 



u 

16 

17 

10 I 

1812 

17 

19 1 

8 19 

20 

2i 

22 

23 

25 

1 1 

27 

27 

40 

IS 19 

*1 Q K1 

1813 

1 

28 

*02 

9*0 

1 

2 

3 

4 

6 

6 

8 

8 

xo 

19 

20 
21 

0(9 

lo 

14 SO 

15 It 

15 56 

1814 

9 

11 b 

Oil 

12 

13 

14 

15 

17 

17 

19 

19 

1815 

20 

22 2 

1 22 

23 

24 

25 

26 

28 

28 

0 

0 

il 

Ol 

10 01 

18 0 

1816 

1 

3 ! 

1 3 

4 

5 

6 

7 

9 

9 

11 

11 

.^4 

25 

aa 

ly lo 

20 31 

0i 

1817 

12 

14 L 

3 14 

15 

16 

17 

18 

20 

20 

22 

22 

27 

28 
29 
29^ 

Ol 

22 21 

0^ Si 

1818 

23 

25 2. 

i 25 

26! 

27 

28 

29 

1 

1 

3 

3 

23 42 

0 ji n 

1819 

4 

6 ^ 

5l 

7 

8 

9 

10 

12 

12 

14 

14 

.44 V 

1820 

15 

17 1< 

5 17 

181 

19 

20 

21 

es 

23 

25 

25 



1821 

26 

28 2’ 

7 28 

29 

0 

1 

2 

4 

4 

6 

6 



1822 

7 

9 S 

5 9 

101 

11 ] 

12 

13 

15 

15 

17 

17 



1823 

18 

20 L 

)20^ 

21 '22 $ 

23 ! 

24 

26! 

26 

28 ‘ 

28 





























































































THE TERRESTRIAL GLOBE. 


245 


Though the preceding table be calculated only for nineteen years, 
it will answer for a century to eome, by changing the years at the expi¬ 
ration of nineteen ; thus, instead of 1805, write 1824, and so on in a 
gradual succession to 1842, without any alteration in the figures under 
the months; and when these years are elapsed, begin again with 
1843, &c. 

To find the time of new moon, subtract the number in the table oppo¬ 
site to the given year, and under the given month, from SO. 

Examples. The time of new moon in March 1820, is on the 14th, 
(=30—16 ;) in December the same year, new moon happens on the 
5th (=30 —25 ;) and so on for any other year and month 

To find the time of full moon, subtract the number in the table op¬ 
posite to the given year, and under the given month, from SO; if the 
remainder be 15, full moon happens on the SOth day of the month ; if 
the remainder exceed 15, the excess above 15 is the day of the month 
on which full moon happens; if the remainder fall short of 15, add 15 to 
it, and the sun will show the day of the month on which full moon will 
happen. 

Examples. Full moon happens on January SO, 1820, (SO—15=»15.) 
In November, 1818, full moon happens on the 12 (SO—S==2T, and 27— 
15=12.) In January, 1818, full moon happens on the 2S (30—23=7, 
and7-|-15=22.) 

At the time of conjunction, or new moon, the sun and moon are in 
the same sign and degree, and the moon’s motion is 12° 11' 6" swifter 
than the apparent motion of the sun (see the note page 74 ;) if this 
difference, therefore, be multiplied by the moon’s age, the product will 
give the number of degrees which the moon’s place is before the sun’s; 
and, as the sun’s place is readily found by the globe, the moon’s place 
will be easily obtained. Likewise, if the place of the moon’s node* be 
given for any particular year, its place for any other year may ?be cal¬ 
culated, the mean annual variation being about 19° 19' 44" (see page 
133.) Hence, the following problem may be solved, though not very 
accurately, without an ephemeris. 


* In a central eclipse of the moon, the moon’s place at the middle of 
the eclipse is directly opposite to the sun, and the moon is then in one 
of her nodes. If the sun’s place in the ecliptic be determined at that 
time by observation, the opposite point will be the true place of the 
moon’s node. 



24G 


PROBLEMS PERFORMED BY 


PROBLEM LV. 

To find the time of the year when the sun or moon will 
be liable to be eclipsed^ 

Ride* 1. Find the place of the moon’s nodes, the 
time of new moon, and the sun’s longitude at that time, 
by an ephemeris then, if the sun be within 17 de¬ 
grees of the moon’s node, there will be an eclipse of the 
sun. 

2. Find the place of the moon’s nodes, the time of 
full moon, and the sun’s longitude at that time, by an 
ephemeris ; then, if the sun’s longitude be within 12 
degrees of the moon’s node, there will be an eclipse of 
the moon. 

Examples. 1. On the 15th of January, 1805, there 
was a full moon, at which time the place of the moon’s 
node was >3 25° 54', and the sun’s longitude >525°; did 
an eclipse of the moon happen at that time ? 

Answer. Here the sun was nearly in the moon’s node, therefore, a 
total eclipse of the moon took place ; for, when the sun is in one of 
the moon’s nodes at the time of full moon, the moon is in the other node, 
and the earth is directly between them; the moon’s place was conse¬ 
quently about 25° in Cancer. 

2. It appears by the foregoing table, that there was a 
new moon on the 30th of January, 1805, at which time 
the place of the moon’s node was >5 25° 16', and the 
sun’s longitude or place was iiC' 10°; was there an eclipse 
of the sun at that time ? 

3. By the foregoing table, or by an ephemeris, there 
was a new moon on the 19th of October, 1808, at which 
time the place of the moon’s node was wl 13® 6', and the 
sun’s longitude ^ 25° 56' ; was there an eclipse of the 
sun at that time ? 

4. On the 3d of November, 1808, there was a full 
moon, at which time the place of the moon’s node wasni, 
12° 18', and the sun’s longitude th. 10° 55'; was there 
an eclipse of the moon at that time ? 

5. On the 4th of April, 1810, there was a new moon, 
at which time the place of the moon’s node was 3^^= 14° 


* White’s Ephemeris, or the Nautical Almanac. 



THE TERRESTRIAL GLOBE. 


247 


5?'and the sun’s longitude T 14° 4', was there an 
eclipse of the sun at that time ? 

6 On the 28lh of September, 1810, there was a new 
moon, at which time the place of the moon’s node was 
^ 5° 32'; and the sun’s longitude =2= 4° 48'; was there 
an eclipse of the sun at that time ? 

PROBLEM LVI. 

To explain the phenomenon of the harvest moon. 

Definition. 1 . The harvest moon, in north latitude, 
is the full moon which happens at, or near, the time of 
the autumnal equinox ; for, to the inhabitants of north 
latitude ; whenever the moon is in Pisces, or Aries (and 
she is in these signs twelve times in a year,) there is very 
little difference between her times of rising for several 
nights together, because her orbit is at these times near¬ 
ly parallel to the horizon. This peculiar rising of the 
moon passes unobserved at all other times of the year 
except in September and October ; for there never can 
be a full moon except the sun be directly opposite to 
the moon : and as this particular rising of the moon can 
only happen when the moon is in X Pisces or T Aries, 
the sun must necessarily be either in riji Virgo or ^ Li¬ 
bra, at that time, and these signs answer to the months 
of September and October. 

Pejinition. 2. The harvest moon, in south latitude, 
is the full moon which happens at, or near, the time of 
the vernal equinox ; for, to the inhabitants of south lati¬ 
tude, whenever the moon is in ^ Virgo or Libra (and 
she is in these signs twelve times in a year,) her orbit is 
nearly parallel to the horizon ; but, when the full moon 
happens in Virgo or =s= Libra, the sun must be either 
in X Pisces or T Aries. Hence, it appears that the har¬ 
vest moons are just as regular in south latitude as they are 
in north latitude, only they happen at contrary times of 
the year. 

Rule for performing the Problem. —1. For north 
latitude. Elevate the north pole to the latitude of the 
the place, put a patch or make a mark in the ecliptic on 


248 


PKOBLKMS PERFORMED BY 


the point Aries, and upon every twelve* degrees pre¬ 
ceding and following that point, till there be ten or eleven 
marks ; bring that mark which is the nearest to Pisces 
to the eastern edge of the horizon, and set the index to 
12 ; turn the globe westward till the other marks suc¬ 
cessively come to the horizon, and observe the hours 
passed over by the index ; the intervals of time be¬ 
tween the marks coming to the horizon will show the di¬ 
urnal difference of time between the moon’s rising. If 
these marks be brought to the western edge of the hori¬ 
zon in the same manner, you will see the diurnal differ¬ 
ence of time between the moon’s setting ; for, when 
there is the smallest difference between the times of the 
moon’s rising,! there will be the greatest difference be¬ 
tween the times of her setting ; and, on the contrary, 
when there is the greatest difference between the times 
of the moon’s rising, there will be the least difference 
between the times of her setting. 

Note. As the moon’s nodes vary their position and form a com¬ 
plete revolution in about nineteen years, there will be a regular period 
of all the varieties which can happen in the rising and setting of the 
moon during that time. The following table (extracted from Ferguson’s 
Astronomy) shows in what years the harvest moons are the least and 
the most beneficial, with regard to the times of their rising, from 1805 to 
1860. The columns of years under the letter L are those in which the 
harvest moons are least beneficial, because they fall about the descend¬ 
ing node ; and these under M are the most beneficial, because they 
fall about the ascending node. 


L 

L 

L 

L 

M 

M 

M 

M 

1807 

18U 

1831 

1847 

1805 

1822 

1838 

1854 

1808 

1815 

1832 

1848 

1806 

1823 

1839 

1855 

1809 

1836 

1833 

1849 

1816 

1824 

1840 

1856 

1810 

1827 

1834 

1850 

1817 

1825 

1841 

1857 

1811 

1828 

1844 

1851 

1818 

1835 

1842 

1858 

1812 

1829 

1845 

1852 

1819 

1836 

1843 

1859 

1813 

1830 

1846 


1820 

1837 

1853 

1860 





1821 





* The reason why you mark every 12 degrees is, that the moon 
gains 12° 11' of the sun in the ecliptic every day ( see the 2d note, p, 

47.) 

t At London when the moon rises in the point Aries, the ecliptic 
at that point makes an angle of only 15 degrees with the horizon ; but, 
when she sets in the point Aries, it makes an angle of 62 degrees ; and, 
when the moon rises in the point Libra, the ecliptic, at that point, 
makes an angle of 62 degrees with the horizon ; but, when she sets in 
the point Libra, it only makes an angle of 15 degrees with the hori¬ 
zon. 




THE TERRESTRIAL GLOBE. 


249 


For south latitude. Elevate (he south pole to the 
latitude of the place, put a patch or make a mark on the 
ecliptic on the point Libra, and upon every twelve de¬ 
grees preceding and following that point, till there be ten 
or eleven marks ; bring that mark which is the nearest 
to Virgo, to the eastern edge of the horizon, and set the 
index to 12; turn the globe westward till the other 
marks successively come to the horizon,and observe the 
hours passed over by the index; the intervals of time 
between the marks coming to the horizon, will be the di¬ 
urnal difference of time between the moon’s rising &;c» 
as in (he foregoing part of (he problem.* 

PROBLEM LVII. 

The day and hour of an eclipse of any one of the satel¬ 
lites of Jupiter being given, to find upon the globe 
all those places where it will be visible. 

Rule. Find the sun’s declination for (he given day, 
and elevate the pole to that declination ; bring the place 
at which the hour is given to the brass meridian, and set 
the index of the hour circle to 12 ; then, if the given 
time be before noon, (urn the globe westward as many 
hours as it wants of noon ; if after noon, (urn the globe 
eastward as many hours as it is past noon ; fix the globe 
in this position : then, 

1. if Jupiter rise after the sun,f (hat is, if he be an 
evening star, draw a line along the eastern edge of the 
horizon with a black lead pencil, this line will pass over 
all places on the earth where the sun is setting at the 
given hour ; turn (he globe westward on its axis till as 
many degrees of the equator have passed under the brass 
meridian as are equal to the difference between the sun’s 
and Jupiter’s right ascension ; keep the globe from re^ 


* This solution is on a supposition that the moon keeps constantly 
in the jcliptic, which is sufficiently accurate for illustrating the prob¬ 
lem. Otherwise the latitude and longitude of the moon, or her right 
ascension and declination, may be taken from the Kphemeris, at the 
time of full moon, and a few days preceding and following it; her place 
will then be truly marked on the globe. 

t Jupiter rises after the sun, wh^en bis longitude is greater than the 
sun’s longitude. 


34 



250 


PROBIiEiMS PEKEOKMED BY 


volving on its axis, and elevate the pole as many degrees 
above the horizon as are equal to J upiter’s declination, 
then draw another line with a pencil along the eastern 
edge of the horizon ; the eclipse will be visible to every 
place between these lines, viz. from the time ot the sun’s 
setting to the time of Jupiter’s setting. 

2. If Jupiter rise before the smw,* that is, if he be a 
morning star, draw a line along the western edge of the 
horizon with a black lead pencil, this line will pass over 
all places of the earth where the sun is rising at the giv¬ 
en hour ; turn the globe eastward on its axis till as ma¬ 
ny degrees of the equator have passed under the brass 
meridian as are equal to the difference between the sun’s 
and Jupiter’s right ascension ; keep the globe from re¬ 
volving on its axis, and elevate the pole as many de¬ 
grees above the horizon as are equal to Jupiter’s decli¬ 
nation, then draw another line with a pencil along the 
western edge of the horizon ; the eclipse will be visible 
to every place between these lines, viz. from the time 
of Jupiter’s rising to the time of the sun’s rising. 

Examples. 1. On the 13lh ol January, 1805, there 
was an emersion of the first satellite of Jupiter at 9 m. 
3 sec. past five o’clock in the morning, at Greenwich ; 
where was it visible ? 

Answer, In this example the longitude of the sun exceeds the lon¬ 
gitude of Jupiter, therefore, Jupiter was a morning star, his declination 
being 19® 16' S. and his longitude 7 signs 29° 46', by the Nautical Al¬ 
manac : his right ascension and the sun^s right ascension may be found 
by the globe ; for. if Jupiter's longitude in the ecliptic be brought to 
the brass meridian, his place w'ill stand under the degree of his declina¬ 
tion ;t and his right ascension will be found on the equator, reckoning 
from Aries. This eclipse was visible at Greenwich, the greater part 
of Europe, the west af Africa, Cape Verd Islands, &c. 

2. On Ihe 8(h of February, 1813, at 9 m. 21 sec. past 
ten o’clock in the evening, at Greenwich, there was 
an emersion of the first satellite of Jupiter ; where was 
the eclipse visible f Jupiter’s longitude at that 


* Jupiter rises before the sun when his longitude is less than the 
sun's longitude. 

t This is on supposition that Jupiter moves on the ecliptic, and, as 
he deviates but little therefrom, the solution by this method will be 
sufficiently accurate. To know if an eclipse of any one af the satel¬ 
lites of Jupiter will be visible at any place ; we are directed by the 
Nautical Almanac, to “ find whether Jupiter be 8® above the horizon 
of the place, and the sun as much below it.'* 



THE TERRESTRIAL GLOBE. 


251 


time being 4 signs 2° 12' ; and his declination 20° 23' 
north. 

3. On the 20th of March, 1813, at 8 m. 32 sec. past 
one o’clock in the morning at Greenwich, there was 
an emersion of the second satellite of Jupiter; where 
was the eclipse visible? Jupiter’s longitude at that 
time being 3 signs 29° 4'; and his declination 21° 5' 
north. 

4. On the 18th of October, 1813, at 52 m. 3 sec. past 
three o’clock in the morning, at Greenwich there was 
an emersion of the first satellite of Jupiter; where 
was the eclipse visible? Jupiter’s longitude at that 
time being 5 signs 3° 41', and his declination 10° 59' 
north. 

5. On the 19th of October, 1813, there was an 
immersion of the second satellite of Jupiter at 53 m. 49 
sec. past 3 o’clock in the morning at Greenwich ; where 
was the eclipse visible ? Jupiter’s longitude at that 
time being 5 signs 3 deg. 41 min. and bis declination 10 
deg. 59 m. north. 

6. On the 10th of November, 1813, there was an 
immersion of the first satellite of Jupiter at 1 min. 16 
sec. past four o’clock in the morning, at Greenwich; 
where was the eclipse visible ? The longitude of 
Jupiter being 5 signs 6 deg. 36 min. and his declination 
9 deg. 58 min. north. 

PROBLEM LVIIL 

To place the terrestrial globe in the sun shine, so that 

it may represent the natural position af the earth* 

Rule. If you have a meridian line* drawn upon a 
horizontal plane, set the north and south points of the 
wooden horizon of the globe directly over this line ; or, 
place the globe directly north and south by the mariner’s 
compass, taking care to allow for the variation ; bring 
the place in which you are situated to the brass meri- 


* As a meridian line is useful for fixing a horizontal dial, and for 
placing a globe directly north and south, &c. the different raethods of 
drawing a line of this kind will precede the problems on dialling. 




252 * 


PROBLEMS PERFORMED BY 


dian, and elevate the pole to it« latitude ; then the globe 
will correspond in every respect vvith the situation of 
the earth itself. The poles, meridians, parallel circles, 
tropics, and all the circles on the globe, will correspond 
with the same imaginary circles in the heavens ; and 
each point, kingdom, and state, will be turned towards 
the real one, which it represents. 

While the sun shines on the globe, one hemisphere 
will be enlightened, and the other will be in the shade : 
thus, at one view, may be seen all places on the earth 
which have day, and those which have night.* 

If a needle be placed perpendicularly in the middle of 
the enlightened hemisphere (which must of course be 
upon the parallel of the sun’s declination for the given 
day,) it will cast no shadow, which shows that the sun is 
vertical at that point ; and if a line be drawn through 
this point from pole to pole, it will be the meridian of the 
place where the sun is vertical, and every place upon 
this line will have noon at that time ; all places to the 
west of this line will have morning, and all places to the 
east of it afternoon. Those inhabitants who are situated 
on the circle which is the boundary between light and 
shade, to the westward of the meridian where the sun is 
vertical, will see the sun rising ; those in the same cir¬ 
cle to the eastward of this meridian will see the sun set¬ 
ting. Those inhabitants towards the north of the cir¬ 
cle which is the boundary between light and shade, will 
perceive the sun to the southward of them, in the hori¬ 
zon ; and those who are in the same circle towards the 
south, will see the sun in a similar manner to the north 

them. 

If the sun shine beyond the north pole at the given 
time, his declination is as many degrees north as he 
shines over the pole ; and all places at that distance 
from the pole will have constant day, till the sun’s de¬ 
clination decreases, and those at the same distance from 
the south pole will have constant night. 


* For this part of the problem it would be more convenient if the 
globe could be properly supported without the frame of it, because the 
shadow of its stand, and that of its horizon, will darken several parts 
'af the surface of the globe, which would otherwise be enlightened. 




THE TERRESTRIAL GLOBE. 


253 


if the sun do not shine so far as the north pole at the 
given time, his declination is as many degrees south as 
the enlightened part is distant from (he pole ; and all 
places within the shade, near the pole will have constant 
night, till the sun’s declination increases northward. 
While the globe remains steady in the position it was 
first placed, when the sun is westward of the meridian, 
you may perceive on the east side of it, in what manner 
the sun gradually departs from place to place as the 
night approaches ; and, when the sun is eastward of the 
meridian, you may perceive on the western side of it, in 
what manner the sun advances from place to place as 
the day approaches. 


PROBLEM LIX. 

The latitude of a place being given, to find the hour of 
the day at any time the sunshines. 

Rule. 1 . Place the north and south points of the 
horizon of the globle directly north and south upon a 
horizontal plane, by a meridian line, or by a mariner’s 
compass, allowing for the variation, and elevate the pole 
to the latitude of the place ; then, if the place be in north 
latitude, and the sun’s declination be north, the sun will 
shine over the north pole : and if a long pin be fixed 
perpendicularly in the direction of the axis of the earth, 
and in the centre of the hour circle, its shadow will fall 
upon the hour of the day, the figure XII of the hour 
circle being first set to the brass meridian. If the place 
be in north latitude, and the sun’s declination be above 
ten degrees south, the sun will not shine upon the 
hour circle at the north pole. 

Rule. 2. Place the globe due north and south upon a 
horizontal plane, as before, and elevate (he pole to the 
latitude of the place ; find the sun’s place in the eclip¬ 
tic, bring it to the brass meridian, and set (he index of 
the hour circle to XII ; stick a needle perpendicularly 
in the sun’s place in the ecliptic, and turn the globe on 
its axis till the needle casts no shadow ; fix the globe in 
this position, and the index will show the hour before 12 
In the morning, or after 12 in the afternoon. 

Rule. 3. Divide the equator into 24 equal parts 
from the point Aries, on which, place the number 


2di PROBLEMS PERFORMED BY 

VI; and proceed westward VII, VIII, IX, X, XI, 
XII, I, II, III, IV, V, VI which will tall upon the point 
Libra, VII, Vili, IX, X, XI, XII, I, II, III, IV, V 
elevate the pole to the latitude, place the globe due 
north and south, upon a horizontal plane, bj a meridian 
line, or a good mariner’s compass, allowing for the va¬ 
riation, and bring the point Aries to the brass meridian ; 
then observe the circle which is the boondary between 
light and darkness westward of the brass meridian, and 
it will intersect the equator in the given hour in the 
morning ; but, if the same circle be eastward of the brass 
meridian, it will intersect the equator in the given hour 
in the afternoon. 

Or, Having placed the globe upon a true horizontal 
plane, set it due north and south by a meridian line; 
elevate the pole to the latitude, and bring the point Aries 
to the brass meridian, as before ; then tie a small string, 
with a noose, round the elevated pole, stretch its other 
end beyond the globe, and move it so that the shadow 
of the string may fall upon the depressed axis ; at that 
instant its shadow upon the equator will give the hour.f 

PBOBLEM LX. 

To find the smi’s altitude, hy placing the globe in the 
sunshine* 

Rule. Place the globe upon a truly horizontal plane, 
stick a needle perpendicularly over the north pole,J in 
the direction of the axis of the globe, and turn the pole 
towards the sun, so that the shadow of the needle may 
fall upon the middle of the brass meridian ; then elevate 
or depress the pole till the needle casts no shadow; for 


♦ On Adams* globes the antarctic circle is thus divided, by which 
the problem may be solved. 

t The learner must remember that the time shown in this problem 
is solar time, as shown by a sun-dial; and therefore, to agree with 
a good clock or watch, it must be corrected by a table of equation of 
time. See a table of this kind among the succeeding problems. 

It would be an improvement on the globes were our instrument- 
makers to drill a very small hole in the brass meridian over the north 
pole. 



THE TERRESTRIAL GLOBE. 


25^} 

then it will point directly to the sun ; the elevation of 
the pole above the horizon will be the sun’s altitude. 

PROBLEM LXI. 

To find the sun^s declination, his place in the ecliptic, 
and his azimuth, by placing the globe in the sun¬ 
shine. 

Rule. Place the globe upon a truly horizontal plane, 
in a north and south direction by a meridian line, and 
elevate the pole to the latitude of the place ; then, if 
the sun shine beyond the north pole, his declination is 
as many degrees north as he shines over the pole ; if the 
sun do not shine so far as the north pole, his declination 
is as many degrees south as the enlightened part is dis¬ 
tant from the pole. The sun’s declination being found,, 
his place may be determined by Prob. XX. 

Stick a needle in the parallel of the sun’s declination^ 
for the given day,* and turn the globe on its axis till the 
needle casts no shadow ; fix the globe in this position, 
and screw the quadrant of altitude over the latitude ; 
bring the graduated edge of the quadrant to coincide 
with the sun’s place, or the point where the needle is 
fixed, and the degree on the horizon will show the azi^ 
muth. 


PROBLEM LXII. 

To draw a meridian line upon a horizontal plane, and 
to determine the four cardinal points of the horizon. 

Rule. 1. Describe several circles from the centre of 
the horizontal plane, in which centre fix a straight wire 
perpendicular to the plane ; mark in the morning where 
the end of the shadow touches one of the circles; in the 
afternoon mark where the end of the shadow touches the 


* On Adams’ globes the torrid zone is divided into degrees by dotted 
lines, 80 that the parallel of the sun’s declination is instantly found : in 
uaing other globes, observe the declination on the brass meridian, and 
stick a needle perpendieularly in the globe under that degree. 




PROBLEMS PERFORMED BY 


2^1) 


same circle ; divide the arc of the circle contained be= 
tween these two points into two equal parts ; a line 
drawn from the point of division to the centre of the 
plane will he a true meridian, or north and south line ; 
and, if this line be bisected by a perpendicular, that 
perpendicular will be an east and west line: thus you 
will have the four cardinal points ; but, to be ver)' ex¬ 
act, the plane must be truly horizontal, the wire must 
be exactly perpendicular to the plane, and the extremi¬ 
ty of its shadow must be compared not only upon one 
of the circles, as above described, but upon several of 
them. 

Rule, 2. Fix a strong straight wire, sharp pointed, at 
the top in the centre of your plane, nearly perpendicu¬ 
lar ; place one end of a wooden ruler on the top of the 
wire, and with a sharp pointed iron pin, or wire, in the 
other end of the ruler, describe an arc of a circle ; take 
otr the ruler from the top of the wire, and observe, at 
two ditferent times of the day, when the shadow of the 
top of the wire falls upon the arc of the circle descri¬ 
bed by the ruler ; mark the two points, and divide the 
arc between them into two equal parts, and draw aline 
from the point of bisection to the centre of your plane; 
this will be a meridian line. 

Rule. 3. Hang up a plumb-line in the sun-shine, so 
that it may cast a shadow of a considerable length, upon 
the horizontal plane, on which you intend to draw your 
meridian line ; draw a line along this shadow upon the 
plane, while at the same time a person takes the altitude 
of the sun correctly with a quadrant, or some other in¬ 
strument answering the same purpose ; then, by knowing 
the latitude of the place, the day of the month, and of 
course the sun’s declination, together with his altitude ; 
find the azimuth, from the north, by spherical trigonome¬ 
try, and substract it from 180^ ; make an angle, at any 
point of the line which was drawn, upon your plane, 
equal to the number of degrees in the remainder, and 
that will point out the true meridian. See Keith’s Trig¬ 
onometry, page 280. 


THE TERRESTRIAI. GLOBE. 


257 


PROBLEM LXm. 

To make a horizontal dial for any latitude. 

Definitions and Observations, —Dialling, or the art 
of constructing dials, is founded entirely on astronomy ; 
and, as the art of measuring time is of the greatest im¬ 
portance, so the art of dialling was formerly held in 
the highest esteem, and th? study of it was cultivated by 
all persons who had any pretensions to science. Since 
the invention of clocks and watches, dialling has not been 
so much attended to, though it will never be entirely ne¬ 
glected ; for, as clocks and watches are liable to stop and 
go wrong, that unerring instrument, a true sun-dial, is 
used to correct and to regulate them. 

Suppose the globe of the earth to be transparent (ag 
represented by Fig. 4. Plate II.) with the hour circles, 
or meridians. &c. drawn upon it, and that it revolves 
round a real axis NS, which is opaque and casts a shad¬ 
ow, it is evident that, whenever the edge of the plane of 
any hour circle or meridian points exactly to the sun, 
the shadow of the axis will fall upon the opposite hour 
circle or meridian. Now, if we imagine any opaque 
plane to pass through the centre of this transparent 
globe, the shadow of half the axis NE will always fall 
upon one side or other of this intersecting plane. 

Let ABCD represent the plane of the horizon of Lon¬ 
don, BN the elevation of the pole or latitude of the place; 
so long as the sun is above the horizon, the shadow of the 
upper half NE of the axis will fall somewhere upon the 
upper side of the plane ABCD. When the edge of the 
plane of any hour circle, as F, G, H, I, K, L, M, O, 
points directly to the sun, the shadow of the axis, which 
axis is coincident with this plane, marks the respective 
hour line upon the plane of the horizon ABCD; the hour 
line upon the horizontal plane is, therefore, a line drawn 
from the centre of it, to that point where this plane in¬ 
tersects the meridian opposite to that on which the sun 
shines. Thus, when the sun is upon F, the meridian of 
London, the shadow of NE the axis will fall upon E, 
XII. By the same method, the rest of the hour lines are 
found, by drawing, for every hour a line from the centre 

35 


25B 


PEOBLE3IS PEBFORMEI> BY 


of the horizontal plane to that meridian, which is diame¬ 
trically opposite to the meridian pointing exactly to the 
sun. If, when the hour circles are thus found, all the 
lines be taken away except the semi-axis NE, what re¬ 
mains will be a horizontal dial for the given place. From 
what has been premised, the following observations nat¬ 
urally arise : 

1. The gnomon of every sun-dial must always be par¬ 
allel to the axis of the earth, and must point diretly to 
the two poles of the world. ■ 

2. As the whole earth is but a point when compared 
with the heavens, therefore, if a small sphere of glass be 
placed on any part of the earth’s surface, so that its axis 
be parallel to the axis of the earth, and the sphere have 
such lines upon it, and such a plane within it as above 
described; it will show the hour of the day as truly as 
if it were placed at the centre of the earth, and the body 
of the earth were as transparent as glass. 

3. In every horizontal dial, the angle, which the style, 
or gnomon, makes with the horizontal plane, must always 
be equal to the latitude of the place for which the dial 
is made. 

Rule for performing the Problem .—Elevate the 
pole so many degrees above the horizon as are equal to 
the latitude of the place ; bring the point Aries to the 
brass meridian ; then, as globes in general* have meri¬ 
dians drawn through every 15 degrees of longitude, 
eastward and westward from the point Aries, observe 
where the meridians intersect the horizon, and note 
the number of degrees between each of them ; the arcs 
between the respective hours will be equal to these de¬ 
grees. The dial must be numbered XII at the brass 
meridian, thence, XI, X, IX, VIII, VII, VI, V, IV, 
&c. towards the west, for morning hours ; and I, IJ, III, 
IV, V, VI, VII, VIII, &c. for evening hours. No 
more hour lines need be drawn than what will answer to 
the suu’^s continuance above the horizon on the longest 


* On Carey’s large globes, the meridians are drawn through every 
ten degrees, an alteration which answers no useful purpose v^atever, 
and is in many cases very inconvenient. To solve this problem, by 
these globes, meridians ranst be drawn through every fifteen degrcei 
with a pencil. 




THE TERRESTRIAL GLOBE. 


259 


Jay at the given place. The style or gnomon of the dial 
must be fixed in the centre of the dial-plate, and make 
an angle therewith equal to the latitude of the place. 
The face of the dial may be of any shape, as round, el¬ 
liptical, square, oblong, &c. &c. 

Example. To make a horizontal dial for the latitude 
of London. 

Having elevated the pole 51^ deg. above the horizon, and brought 
the point Aries to the brass meridian, you will hnd the meridians on 
the eastern part of the horizon, reckoning from 12, to be 11° 50', 24* 
20', ^8° S', 5S° 35', 71° 6'; and 90° for the hours I, II, III, IV, V, and 
VI; or, if you count from the east towards the south, they will be 0% 
18° 54', 36° 25', 51° 57', 65° 40', and 78° 10', for the hours VI, V, IV, 
III, II, I, reckoning from VI o’clock backArard to XII. There is no 
occasion to give the distance farther than VI, because the distances 
from XII to VI in the forenoon are exactly the same as from XII to 
VI in the afternoon ; and hour lines continued through the centre of 
the dial are the hours on the opposite parts thereof. 

The following Table, calculated by spherical trigonometry, contains 
not only the hour arcs, but the halves and quarters from Xll to VJ, 


Hours. 

Hour 

Angles. 

Hour 

Arcs. 

Hours. 

Hour 

Angles. 

Hour 

Arcs. 

XII. 

0» O' 

0° 0' 

Si 

48° 45' 

41° 45' 

m 

3 45 

2 56 

Si 

52 SO 

45 34 

12i 

7 SO 

5 52 

3i 

56 15 

49 SO 

12 I 

11 15 

8 51 

IV. 

60 

0 

53 35 

I 

15 

0 

11 50 

4i 

63 45 

57 47 

u 

18 45 

14 52 

4i 

67 SO 

62 

6 

H 

22 30 

17 57 

H 

71 15 

66 S3 


26 15 

21 

6 

V. 

75 

0 

71 

6 

II. 

SO 

0 

24 20 

5i 

78 45 

7.5 45 

2i 

33 45 

27 36 

H 

82 SO 

80 25 

III. 

37 30 

31 

0 

5| 

86 15 

85 IS 

41 15 

45 0 

34 28 

38 S 

VI. 

90 

0 

90 

0 


The calculation of the hour arcs by spherical trigonometry is extreme* 
ly easy ; for while the globe remains in the position above described; it 
will be seen that a right-angled spherical triangle is formed, the per¬ 
pendicular of which is the latitude, its base the hour arc, and its verij- 
cal angle the hour angle. Hence, 

Radius, sine of 90° 

Is to sine of the latitude ; 

As tangent of the hour angle, 

Is to the tangent of the hour arc on the horusqfn. 












260 


PROBLEMS PERFORMED BY 


It may be observed here, that if a horizontal dial, which show.i the 
hour by the top of the perpendicular gnomon, be made for a place in 
the torrid zone, whenever the sun’s declination exceeds the latitude of 
the place, the shadow of the gnomon will go back twice in the day, 
once in the forenoon, and once in the aftemoon ; and the greater the 
difference between the latitude and the sun’s declination is, the farther 
the shadow will go back. In the S8th chapter of Isaiah, Hezekiah is 
promised that his life shall be prolonged 15 years, and as a sign of this, 
he is also promised that the shadow of the sun-dial of Ahaz shall go back 
ten degrees. This was truly, as it was then considered, a miracle; for, 
as Jerusalem, the place where the dial of Ahaz was erected, was out of 
the torrid zone, the shadow could not possibly go back from any natu¬ 
ral cause. 


PROBLEM LXIV. 

To make a vertical dial, facing the sotilhy in north lati¬ 
tude, 

'Definitions and Observations, —The horizontal dial, 
as described in.tlie preceding problem, was supposed to 
be placed on a pedestal, and as the sun always shines 
upon such a dial when he is above the horizon, provided 
no object intervene, it is the most complete ofall kinds 
of dials. The next in utilily is the vertical dial facing 
the south in north latitudes ; that is, a dial standing a- 
gainst the wall of a building which exactly faces the 
south. 

Suppose the globe to be transparent, as in the fore¬ 
going problem (see Figure 5, Plate II.) with the hour 
circles or meridians, F, G, H, I, K, L, M, O, &c. drawn 
upon it; ADCB an opaque vertical plane perpendicular 
to the horizon, and passing through the centre of the 
globe. While the globe revolves round its axis NS, it 
is evident that, if the semi-axis ES be opaque and casta 
shadow, this shadow will always fall upon the plane 
ABC, and mark out the hours as in the preceding prob¬ 
lem. By comparing Fig. 5 with Fig. 4, in Plate II, it 
will appear that the plane surface of every dial whatev¬ 
er, is parallel to the horizon of some place or other upon 
the earth, and that the elevation of the style or gnomon 
above the dial’s surface, when it faces the south, is al¬ 
ways equal to the latitude of the place whose l^orizon is 
parallel to that surface. Thus it appears that SP^ which 
IS the co-latitude of London, is the latitude of the place 
whose horizon is represented by the plaije^DCB : for, 


THE TERRESTRIAL GLOBE. 


2t)i 


let the south pole of the globe be elevated 38^ degrees 
above the southern point of the horizon, and the point 
Aries be brought to the brass meridian ; then, if the 
globe be placed upon a table, so as to rest on the south 
point of the wooden horizon, it will have exactly the ap¬ 
pearance of Fig. 5, Plate 'II. the wooden horizon will 
represent the opaque plane ADCB, the south point will 
be at B, and the north point at D under London, the east 
point at C, and the west point at A. Hence, we have the 
following: 

Rule for performing the problem. —If the place be in 
north latitude, elevate the south pole to the complement 
of that latitude; bring the point Aries to the brass meri¬ 
dian ; then, supposing meridians to be drawn through 
every 15° of longitude, eastward and westward from the 
point Aries (as it is generally the case ;) observe where 
these meridians intersect the horizon, and note the num¬ 
ber of degrees between each of them ; the arcs between 
the respective hours will be equal to these degrees. The 
dial must be numbered XII at the brass meridian, thence, 
XI, X, IX, VIII, VII, VI, towards the west, for morn 
ing hours; and I, II, III, IV, V, VI, towards the east, 
for evening hours. As the sun cannot shine longer upon 
such a dial as this than from VI in the morning to VI in 
the evening, the hour lines need not be extended any 
farther. 

Example. To make a vertical dial for the latitude 
of London. 

Elevate the south pole 58^ degrees above the horizon, and bring the 
point Aries to the brass meridian ; then the meridians will intersect the 
horizon, reckoning from the south towards the east, in the following 
degrees ; 9° 28', 19® 45', 31® 54', 47® 9', 66° 42', and 90“, for the hours 
I, II, 'III, IV, V, VI; or, if you count from the east towards the 
south,'they will be O’, 23® 18', 42® 51', 58® 6', 70° 15',S80° 32', for the 
hours VI, V, IV, III, II, I. The distances from XII to VI in the fore¬ 
noon are exactly the same as the distances from XII to VI in the after¬ 
noon. 

The following table contains not only the hour arcs, but the halves 
and quarters from XTI to VI; it is calculated exactly in the same man¬ 
ner as the table in the preceding problem, using the complement of th* 
latitude instead of the latitude. 


PROBLEMS PERFORMED BY 


2(i2 


Hours. 

Hour 

Angles. 

Hour 

Arcs. 

Hours. 

Hour 

Angles. 

Hour 

Arcs. 

XII. 

0° 

0' 


O' 

H 

48® 

45' 

35® 

22' 

12J 

3 

45 

2 

20 

Si 

52 

SO 

39 

3 

m 

7 

so 

4 

41 

H 

56 

15 

42 

58 

12| 

11 

15 

7 

3 

IV. 

60 

0 

47 

9 

I. 

15 

0 

9 

28 

4i 

63 

45 

51 

S6 

n 

18 

45 

11 

56 

H 

6T 

SO 

56 

20 

H 

22 

SO 

14 

2T 


71 

15 

61 

23 

H 

26 

15 

IT 

4 

V. 

75 

0 

66 

43 

11. 

30 

0 

19 

45 

H 

78 

45 

72 

17 


S3 

45 

22 

35 


82 

SO 

78 

S 

U 

ST 

SO 

25 

32 

H 

86 

15 

84 

0 


41 

15 

28 

S3 

VI. 

90 

0 

90 

0 

III. 

45 

0 

SI 

54 







The student will recollect that the lime shewn by a sun-dial is not 
the exact time of the day, as shown by a watch or clock, (see Defini¬ 
tion! 55, 56, and 57, page 1:2.) A good clock measures time equally, 
but a sun-dial (though used for regulating clocks and watches) measures 
time unequally. The following table will show to the nearest minute 
how much a clock should be faster or slower than a sun-dial; such s. 
table should be put upon every horizontal sun-dial. 




1 




















THE TERRESTRIA.L GLOBE. 


263 




rs 


rs 


•3 


C3 tn 


a m 


s ^ 

m 

c 


C0 SS 

a> 

eS js 


cd ^ 

V 

« rf: 


^ ca 

3 

a 


3 

S 

E'l 

3 

C 

ua 

5 

CO o 

s 

Q 




g 

RS 

s 

pg 

i 

Jan. 1 

4 

April 1 

4^^ 

Aug. 9 

5 r 

27 

16 

S 

5 

4 

sg 

15 

Ag 

Nov. 15 

15 

5 

6 

7 

2^ 

20 

3^ 

20 

14 

7 

7 

11 

1 E 

24 

2p- 

24 

ISf^ 

9 

8 

15 

0 » 

28 

1* 

27 

12 g 

12 

9r5 

* 


31 

0~ 

SO 

11 ^ 

15 

log 

19 

i 

* 


Dec. 2 

10 §• 

18 

11 

24 

X 

2 O 

Sep. 3 

1 

5 

9? 

21 

12 5^ 

30 

« o* 

6 


7 

8" 

25 


May 13 

^ o 

3 o 

9 

3? 

9 

7S- 

31 

Feb. 10 

15^ 

29 

June 5 

12 

15 

5v, 

11 

13 

6g 
5 ^ 

21 

27 

14 = 

10 

15 

17’ 

0 

18 

21 

6® 

7^ 

16 

18 

4® 

3 5 

Mar. 4 


« 

24 

8Z 

20 

2 2- 

8 


20 

1 

27 

9^" 

22 

1 ’ 

12 

10“ 

25 

t ^ 

2® 
'Z ® 

4S^ 

SO 

10 = 

24 

0 

15 

9 

29 

Oct. 3 

11| 

« 


19 

8 

July 5 

6 


26 

1 c 

22 

7 

11 

10 

13^ 

28 


25 

6 

28 

D 

14 

14- 

SO 

3% 

28 

5 


o • 

19 

15 


cc 









Dials may be constructed on all kinds of planes, whether horizontal 
or inclined: a vertical dial may be made to face the south, or any point 
of the compass ; but the two dials already described are the most useful. 
To acquire a complete knowledge of dialling, the gnomonical projec¬ 
tion of the sphere, and the principles of spherical trigonometry must 
be thoroughly understood ; these prelerainary branches may be learned 
from Emerson’s Gnomonical Projection, and Keith’s Trigonometry. 
The writers on dialling are very numerous; the last and best treatise 
on this subject is Emerson’s. 



























264 


PKO«LEMS PERFOKMED HY 


CHAPTER 11. 

Problems performed by the Celestial Globe, 


PROBLEM LXV. 

To find the right ascension and declination of the siiUy^ 
or a star. 


Rule, Bring the sun or star to that part of the brass 
meridian which is numbered from the equinoctial towards 
the poles; the degree on the brass meridian is the de¬ 
clination, and the number of degrees on the equinoctial, 
between the brass meridian and the point Aries, is the 
right ascension. 

Or, Place both the poles of the globe in the hori¬ 
zon, bring the sun or star to the eastern part of the hori¬ 
zon ; then the number of degrees which the sun or star 
is northward or southward of the east, will be the decli¬ 
nation north or south; and the degrees on the equinoc¬ 
tial, from Aries to the horizon, will be the right ascen¬ 


sion. 

Examples, I. Required the right ascension and de* 
clination of a Dubhe, in the back of the Great Bear. 
Answer. Right Ascension 162° 49', declination 62* 48' N. 


2. Required the right 
the following stars, 
y, Algenih^ in Pegasus, 
fit, Scheder, in Cassiopeia. 

Mirach, in Andromeda, 
fit, Achcrner, in Eridanus. 
fit, Mmkar, in Cetus. 

Algols in Perseus, 
fit, Aldebaratiy in Taurus, 
fit, CapeUtty in Auriga. 


ascension and declinations of 

/3, Rigel, in Orion, 
y, BellatriXy in Orion, 
fit, Betelguese^ in Orion, 
fit, Canopus^ in Argo Navis, 
fit, Procyon, in the Little Dog. 
y, Algoraby in the Crow, 
at, Arcturus, in Bootes, 
ff, Vendemiatrixy in Virgo. 


* The right ascension and declinations of the moon and the plan¬ 
ets must be found from an ephemeris; because, by their continual 
change of situation, they cannot be placed on the celestial globe, as the 
stars are placed. 




IHE CELESTIAL GLOBE. 


265 


PROBLEM LXVI. 


To find the latitude and longitude of a star,^ 


Rule* Place the upper end of the quadrant of alti-* 
tude on the north or south pole of the ecliptic, accord¬ 
ing as the star is on the north or south side of the eclip¬ 
tic, and move the other end till the star comes to the 
graduated edge of the quadrant; the number of degrees 
between the ecliptic and the star is the latitude ; and the 
number of degrees on the ecliptic, reckoned eastward 
from the point Aries to the quadrant, is the longitude. 

Or, elevate the north or south pole 66|° above the 
horizon, according as the given star is on the north or 
south side of the ecliptic ; bring the pole of the ecliptic 
to that part of the brass meridian which is numbered 
from the equinoctial towards the pole ; then the ecliptic 
will coincide with the horizon ; screw the quadrant of 
altitude upon the brass meridian over the pole of the 
ecliptic : keep the globe from revolving on its axis, and 
move the quadrant till its graduated edge comes over 
the given star: the degree on the quadrant cut by the 
star is its latitude ; and the sign of the degree on the e- 
cliptic cut by the quadrant shows its longitude. 

Examples. 1. Required the latitude and longitude 
oi ot Aldebaran in Taurus. 

Answer. Latitude 5® £8' S. longitude 2 signs 6® 53'; or 6® 53' in 
Gemini. 

2. Required the latitudes and longitudes of the fol’ 


lowing stars. 

Markab, in Pegasus. 

/0, Scheat, in Pegasus. 

«, Fomalhaut, in the S. Fish. 
Deneb, in Cygnus. 

Altair^ in the Eagle. 
i3, Albireo^ in Cygnus. 


Vega, in Lyra, 
y, Rastaben, in Draco. 

<t, Antares, in the Scorpion. 
«e, Arcturus, in Bootes. 

/3, Pollux^ in Gemini, 

Rigel^ in Orion. 


* The latitudes and longitudes of the planets must be found from 


ephemeris. 


36 




266 


PROBLEMS PERFORMED BY 


PROBLEM LXVIL 

The right ascension and declination of a star, the 
mooiiy a planety or of a comety being given, to find its 
place on the globe* 


Rule. Bring the given degrees of right ascension to 
that part of the brass meridian which is numbered from 
the equinoctial towards the poles; then, under the given 
declination on the brass meridian, you will find the star, 
or place of the planet. 

Examples. 1 . What star has 261° 29' of right as¬ 
cension, and 52° 27' north declination ? 

Answer. ^ in Draco. 

2. On the 20th of August, 1805, the moon’s right as¬ 
cension was 91° 3' and her declination24°48' ;findher 
place on the globe at that time. 

Answer. In the Milky Way, a little above the left foot of Castor. 

3. What stars have the following right ascensions and 
declinations f 


ight Ascensions. 

Declinations. 

Right Ascensions. 

Declinations. 

7° 

19' 

55° 26' N. 

83° 

6' 

34°11'S. 

11 

11 

59 38 N. 

86 

13 

44 55 N. 

25 

54 

19 50 N. 

99 

5 

16 26 S. 

46 

32 

9 34 S. 

no 

27 

32 19 N. 

53 

54 

23 29 N. 

113 

16 

28 30 N. 

76 

14 

8 27 S. 

129 

2 

7 8 N. 


4. On the first of December, 1813, the moon’s right 
ascensional midnight was 352° 21', and her declina¬ 
tion 17° 25/ S. ; find her place on the globe. 

5. On the first of May, 1805, the declination of Venua 
was 11°41' N. and her right ascension 31° 30'; find her 
place on the globe at that time. 

6. On the 19th of January, 1805, the declination of 
Jupiter was 19° 29' south, and his right ascension 238°;. 
find his place on the globe at that time.. 



the celestial globe. 


267 


PROBLEM LXVIII. 


The latitude and longitude of the moony a stavy or a 
planet being giveUy to find its place on the globe. 

Rule* Place the division of the quadrant of altitude 
marked O, on the given longitude in the ecliptic, and the 
upper end on the pole of the ecliptic ; then under the 
given latitude, on the graduated edge of the quadrant, 
you will find the star, or place of the moon, or planet. 

Examples. 1. What star has 0 signs 6° 16' of lon¬ 
gitude, and 12® 36' N. latitude ? 

Answer, y in Pegasus. 

2. On the 5th of June, 1813, at midnight, the'moon’s 
longitude was 5* 16° 8', and her latitude 2° 51' N : 
find her place on the globe. 

3. What stars have the following latitudes and longi¬ 
tudes ? 


Latitudes. 

12® 35' S. 
5 29 N. 

31 8 S. 

22 52 N. 
16 3 S. 


Longitudes. 

1* 11® 25' 
2 6 53 

2 13 56 

2 18 57 
2 25 51 


Latitudes. 

390 33' S. 
10 4 N. 

0 27 N. 
44 20 N. 
•21 6 S. 


Longitudes. 
3* 11® 13' 

3 ir 21 

4 26 57 

r 9 22 

11 0 56 


4. On the first of June, 1813, the longitudes and lati¬ 
tudes of the planets were as follows; required their 
places on the globe. 


Longitudes. 

V 19® 42' 

Latitudes. 

2 ® 20' S. 

2 / 

Longitudes. 

4‘ 5® 19' 

0'> 

Latitudes. 
42' N. 

2 12 26 

0 

0 s. 

h 

9 18 30 

0 

21 N. 

10 7 35 

2 

59 S. 

¥ 

7 25 20 

0 

14 N. 


PROBLEM LXIX. 


The day and hotiTy and the latitude of a place being 
given y to find what stars are risingy seltingy culmina- 
iingy &c. 

Rule. Elevate the pole to the latitude of the place^ 
find the sun’s place in the ecliptic, bring it to the brass 




268 


PROBLEMS PERFORMED Hfc- 


meridian) and set the index of the hour circle to Iti; 
then, if the time be before noon, turn the globe eastward 
on its axis till the index has passed over as many hours 
as the time wants of noon; but, if the time be past noon, 
turn the globe westward till (he index has passed over as 
many hours as the time is past noon; then all the stars 
on the eastern semi circle of the horizon will be rising, 
those on the western semi-circle will be setting, those 
under the brass meridian above the horizon will be cul¬ 
minating, those above the horizon will be visible at the 
given time and place, those below will be invisible. 

If the globe be turned on its axis from east to west, 
those stars which do not go below the horizon never set 
at the given place ; and those which do not come above 
the horizon never rise; or, if the given latitude be sub¬ 
tracted from 90 degrees, and circles be described on the 
globe, parallel to the equinoctial, at a distance from it 
equal to the degrees in the remainder, they will be the 
circles of perpetual apparition and occultation. 

Examples. 1. On the 9th of February, when it is 
nine o’clock in the evening at London, what stars are 
rising, what stars are setting, and what stars are on the 
meridian ? 

Answer. Alphacca in the northern Crown is rising; Arcturus 804 ! 
Mirach in Bootes just above the horizon ; Sirius on the meridian ; Pro- 
cyon and Castor and Pollux a little east of the meridian. The constel¬ 
lations Orion, Taurus, and Auriga, a little west of the meridian; Mark- 
ab in Pegasus just below the western edge of the horizon, &c. 

2 . On the 20th of January, at two o’clock in the morn¬ 
ing at London, what stars are rising, whai stars are set¬ 
ting, and what stars are on the meridian ? 

Answer. Vega in Lyra, the head of the Serpent, Spica, Virginus, 
&c. are rising; the head of the Great Bear, the Claws of Cancer, &c. 
on the meridian; the head of Andromeda, the neck of Cetus, and the 
body of Coluraba Noachi, &c. are setting. 

3. At ten o’clock in the evening at Edinburgh, on the 
15th of November, what stars are rising, what stars are 
setting, and what stars are on the meridian ? 

4. What stars do not set in the latitude of London, 
and at what distance from the equinoctial is the circle of 
perpetual apparition ? 

5. What stars do not rise to the inhabitants of Edin¬ 
burgh ? and at what distance from the equinoctial is (he 
circle of perpetual occultation? 


the celestial globe. 269 

G. What stars never rise at Otaheite, and stars 
never set in Jamaica ? 

7, How far must a person travel southward fri^ 
don to lose sight of the Great Bear ? 

8 . What stars are continually above the hori^n at 
the north pole, and what stars are constantly belo\the 
horizon thereof ? 


PROBLEM LXX. 

The latitude of a place, day of the month, and hour 
being given, to place the globe in such a manner as 
to represent the heavens at that time ; in order to find 
out the relative situations and names of the constella^ 
Hons and remarkable stars. 

Rule. Take the globe out into the open air, on a 
clear star-light night, where the surrounding horizon is 
uninterrupted by different objects; elevate the pole to 
the latitude of the place, and set the globe due north 
and south by a meridian line, or by a mariiMf’s compass, 
taking care to make a proper allowance for fhe variation ; 
find the sun’s place in the ecliptic, bring it to the brass 
meridian, and set the index of the hour circle to 12 ; then 
if the time be after noon, turn the globe westward on its 
axis till the index has passed over as many hours as the 
time is past noon ; but, if the time be before noon, turn 
the globe eastward till the index has passed over as ma¬ 
ny hours as the time wants of noon : fix the globe in this 
position, then the flat end of a pencil being placed on 
any star on the globe, so as to point towards the centre, 
the other end will point to that particular star in the 
heavens. 


PROBLEM LXXI. 

To find when any star, or planet, will rise, come to 
the meridian, and set at any given place. 

Rule. Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the place; find the 
sun’s place in the ecliptic, bring it to the brass meridian, 
and set the index of the hour circle to 12. Then, if the 


270 ^ROULEMS PERFORMED BY 

star* or be below the horizon, turn the globe 

westwar^^* *be star or planet comes to the eastern 
part of/® horizon, the hours passed over bj the index 
will sh^ Ibe time from noon when it rises ; and, by 
contifbig the motion of the globe westward till the star, 
&c.1® Ihe meridian, and to the western part of 
the tjrizon successively, the hours passed over by the 
inept will show the time of culminating and setting. 

X the star, &c. be above the horizon and east of the 
/eridian, find the time of culminating, setting, and ris- 
/ig, in a similar manner. If the star, Sec. be above the 
aorizon west of the meridian, find the time of setting, 
Rising, and culminating, by turning the globe westward 
on its axis. 

Exainples. 1. At what time will Arcturus rise, come 
to the meridian, and set at London, on the Tth of Sep-- 
tember ? 

Answer. It will rise at seven o’clock in the morning, come to the 
meridian at three in the afternoon, and set at eleven o’clock at night. 

2. On the first of August, 1305, the longitude of Ju¬ 
piter was 7 signs 26 deg. 34 min. and his latitude, 45 
min. N. at \t^at time did he rise, culminate and set, at 
Greenwich, and was he a morning or an evening 
star. ? 

Answer. Jupiter rose at half past two in the after noon, came to 
the meridian at about ten minutes to seven, and set at a quarter past 
eleven in the evening. Here Jupiter was an evening star, because he 
set after the sun. 

3. At what time does Sirius rise, set, and come to the 
meridian at London, on the 31st of January ? 

4. On the 1st of January, 1813, the longitude of Ve¬ 
nus was 8 signs 5 deg. 55 min. and her latitude 1 deg. 
41 raiI^^ N. at what time did she rise, culminate, and 
set at Greenwich, and was she a morning or an eve¬ 
ning star ? 

5. At what time does Aldebaran rise, come to the 
meridian, and set at Dublin, on the 25th of November ? 

6. On the first of February, 1813, the longitude of 
Mars was 8 signs 3 deg. 40 min. and latitude 0 deg. 
36 min. N. at what time did he rise, set, and come to 
the meridian at Greenwich ? 


* The latitude and longitude (or the right ascension and declination) 
jof the planet, must be taken from an ephemeris, and its place on the 
globe must be determined by Prob. LXVIII (or LXVII.) 




THE CELESTIAL GLOBE. 


271 


PROBLEM LXXII. 


To find the amplitude of any star, its oblique oscoi- 
sion and descension, and its diurnal arc, for an^ 
given day. 


Rule> Elevate the pole to the latitude of the place, 
and bring the given star to the eastern part of the hori¬ 
zon ; then the number of degrees between the star and 
the eastern point of the horizon will be its rising am¬ 
plitude ; and the degree of the equinoctial cut by the 
horizon will be the oblique ascension ; set the index of 
the hour circle to 12, and turn the globe westward till the 
given star comes to the western edge of the horizon; 
the hours passed over by the index will be the starts 
diurnal arc, or continuance above the horizon. The 
setting amplitude will be the number of degrees between 
the star and the western point of the horizon, and the 
oblique descension will be represented by that degree 
of the equinoctial which is intersected by the horizon, 
reckoning from the point Aries. 

Examples. 1. Required the rising and setting ampli¬ 
tude of Sirius, its oblique ascension, oblique descension, 
and diurnal arc, at London. 

Answer. The rising amplitude is 27 deg. to the south of the east; 
setting amplitude 27 deg. south of the west; oblique ascension 120 deg.; 
oblique descension 77 deg.; and diurnal arc 9 hours 0 minutes 

2 . Required the rising and setting amplitude of Alde- 
baran, its oblique ascension, oblique descension, and 
diurnal arc, at London. 

3. Required the rising and setting amplitude of Arc- 
turus, its oblique ascension, oblique descension, and 
diurnal arc, at London. 

4. Required the rising and setting amplitude of y 
Bellatrix, its oblique ascension, oblique descension, and 
diurnal arc, at London. 


PROBLEM LXXIII. 

The latitude of a place given, to find the time of the year 
at which any known star rises or sets acronycally, 
that is,'when it rises or sets at sun-setting. 

Buie. Elevate the pole to the latitude of the place, 
bring the given star to the eastern edge of the horizon, 


272 


PROBLEMS PERFORMED BY 




X- - 


and observe what degree of the ecliptic is intersected by 
the western edge of the horizon, the day of the month 
answering to that degree will show the time when the 
star rises at sun-set, and consequently, when it begins to 
be visible in the evening. Turn the globe westward on 
its axis till the star comes to the western edge of the 
horizon, and observe what degree of the ecliptic is in¬ 
tersected by the horizon, as before; the day of the 
month answering to that degree will show the time when 
the star sets with the sun, or when it ceases to appear 
in the evening. 

Examples, 1. At what time does Arcturus rise 
acronycally at Ascra* in Bcetia, the birth-place of 
Hesiod; the latitude of Ascra, according to Ptolemy, 
being 37 deg. 45 min. N ? 

Answer. AVhen Arcturus is at the eastern part of the horizon, the 
eleventh degree of Aries will be at the western part answering to the 
first of April,t the time when Arcturus rises acronycally : and it will 
set acronycally on the 30th of November. 

2. At what time of the year does Aldebaran rise 
acronycally at Athens, in 38 deg. N. latitude ; and at 
what time of the year does it set acronycally ? 

3. On what day of the year does y in the extremity of 
the wing of Pegasus rise acronycally at London ; and on 
what day of the year does it set acronycally ? 

4. On what day of the year does e in the right foot of 
Lepus rise acronycally at London ? And on what day of 
the year does it set acronycally ? 


* See page 14. 

t Hence, Arcturus now rises acronycally in latitude 37® 45' N. a- 
about 100 days after the winter solstice. Hesiod, in his Opera & Dies, 
lib. ii. verse 185, says : 

When from the solstice sixty wintry days 

Their turns have finished, mark, with glitt’ring rays, 

From Ocean’s sacred flood, Arcturus rise, 

Then first to gild the dusky evening skies. 

Here is a difference of 40 days in the achronical rising of this star 
(supposing Hesiod to be correct) between the time of Hesiod and the 
present time; and as the day answers to about 59' of the ecliptic (see 
the note page IS,) 40 days will answer to 39 deg.; consequently, the 
winter solstice in the time of Hesiod was in the 9th deg. of Aquarius. 
Now, the recession of the equinoxes is about 50^' in a year ; hence, 
50|" : 1 year ; : 39® ; 2794 years since the time of Hesiod ; so that 
he lived 990 years before Christ, by this mode of reckoning. Lem- 
priere, in his Classical Dictionary, says Hesiod lived 907 years before 
Christ. 



THE CELESTIAL GLOBE. 


273 


PROBLEM LXXIV. 

The latitude of a place giveuy to find the time of the 
year at which any known star rises or sets cosmicaU 
ly, that is, when it rises or sets at sun-rising. 


Rule. Elevate the pole to the latitude of the place, 
bring ilie given star to the eastern edge of the horizon, 
and observe what sign and degree of the ecliptic are in¬ 
tersected by the horizon ; the month and day of the 
mouih, answering to that sign and degree, will show the 
time when the star rises with the sun. Turn the globe 
westward on its axis till the star comes to the western 
edge of the horizon, and observe what sign and degree 
of the ecliptic are intersected by the eastern edge, as 
before ; these will point out on the horizon, the time 
when the star sets at sun-rising. 

. Examples. 1. At what time of the year do the 
Pleiades set cosmically at Miletus in Ionia, the birth¬ 
place of Thales; and at what time of the year do they 
rise cosmically; the latitude of Miletus, according to 
Ptolemy, being 37 deg. N. ? 

Answer. The Pleiades rise with the sun on the 10th of May, anA 
they set at the time of sun-rising on the 22d of November.* 

2. At what time of the year does Sirius rise with the 
sun at London ; and at what time of the year will Sirius 
set when the sun rises ? 


* Pliny says (Nat. Hist. lib. xviii. chap. 25.) that Thales determined 
the cosrnical setting of the Pleiades to be twenty-five days after the au¬ 
tumnal equinox. Supposing this observation to be made at Miletus, 
there will be a difference of thirty-five days in the cosrnical setting of 
this star since the time of Thales ; and, as a day answers to about 59' 
of the ecliptic, these days will make about Si’’25'; consequently, in 
the time of Thales, the autumnal equinoctial colure passed through 4® 
35' of .Scorpio ; and, as before, 50^" : 1 year : : 34® 25' ; 2465 years 
since the time of Thales, so that Thales lived (2465—1804) 661 years 
before the birth of Christ. According to Sir Isaac Newton’s Chronolo¬ 
gy, Thales flourished 396 before Christ. Thales was well skilled in ge¬ 
ometry, astronomy, and philosophy; he measured the height and extent 
of the Pyramids of Egypt, was the first who calculated with accuracy, a 
solar eclipse : he discovered the solstices and equinoxes, divided the 
heavens into five zones, and recommended the division of the year into 
365 days. Miletus was situated in Asia Minor, south of Ephesus, and 
south east of the island of Samos. 

37 



274 


PROBLEMS PERFORMED BY 


3 . At what time of the year does Menkar, in the jaw 
of Ce(us, rise with the sun, and at what time does it set 
at sun-rising at London ? 

4 . At what time of the year does Procyon, in the 
Little Dog, set when the sun rises at London, and at 
what time of the year does it rise with the sun ? 

PROBLEM LXXV. 

To find the time of the year when any given star rises 
or sets hetiacally,^ 

iiule* The heliacal rising and setting of the stars 
will vary according to their different degrees of magni¬ 
tude and brilliancy ; for it is evident that, the brighter a 
star is when above the horizon, the less the sun will be 
depressed below the horizon when the star first becomes 
visible. According to Ptolemy, stars of the first mag¬ 
nitude are seen rising and setting when the sun is 12 
degrees below the horizon ; stars of the second magni¬ 
tude require the sun’s depression to be thirteen degrees ; 
stars of the third magnitude fourteen degrees, and soon, 
reckoning one degree for each magnitude. This being 
premised: 

To solve the Problem. Elevate the pole so many 
degrees above the horizon as are equal to the latitude 
of the place, and screw the quadrant of altitude on the 
brass meridian over that latitude ; bring the given star to 
the eastern edge of the horizon, and move the quadrant 
of altitude till it intersects the ecliptic twelve degrees 
below the horizon, if the star be of the first magnitude ; 
thirteen degress, if the star be of the second magnitude ; 
fourteen degrees, if it be of the third magnitude &c. ; 
the point of the ecliptic, cut by the quadrant, will show 
the day of the month, on the horizon, when the star rises 
heliacally. Bring the given star to the western edge of 
the horizon, and move the quadrant of altitude till it in¬ 
tersects the ecliptic below the western edge of the hori¬ 
zon, in a similar manner as before ; the point of the 


* See Definition 89 page 22, 



THE CELESTIAL GLOBE. 275 

ecliptic cut bj the quadrant will show the day of the 
month, on the horizon, when the star sets heliacaiiy. 

Examples, 1. At what time does /3 Tauri, or the 
bright star in the Bull’s Horn, of the second magnitude, 
rise and set heliacaiiy at Rome ? 

Answer. The quadrant will intersect the od of Cancer 13 deg. be¬ 
low the eastern horizon, answering to the ^24th of June ; and the 7tli 
of Gemini 13 deg. below the western horizon, answering to the 28th of 
May. 

2. At what time of the year does Sirius, or the 
Dog Star, rise heliacaiiy at Alexandria in Egypt ; and 
at what time does it set heliacaiiy at (he same place ? 

Answer. The latitude of Alexandria is 31 deg 13 min. north ; the 
quadrant will intersect the 12th of Leo. 12 deg below the eastern hori¬ 
zon, answering to the 4th of August ;* and on the second ofUeitiini, 12 
deg below the western horizon, answering to the 23d of iVlay. 

3. At what time of the year does Arciui us rise heli- 
acally at Jerusalem, and at what time does it set heli- 
aeally ? 

4. At what time of the year does Cor Hydiae rise and 
set heliacaiiy at London ? 


* The ancients reckoned the beginning of the Dog Days from th& 
heliacal rising of Sirius, and their continuance to be ab<»ut 40 days. 
Hesiod informs us, that the hottest season of the year (Dog Days) ended 
about 50 days after the summer solstice. We have determined in the 
note of Example 1. Prob. LXXIII. (though perhaps not very accu¬ 
rately,) that the winter solstice in the time of Hesiod, was in the 9tb 
degree of Aquarius; consequently, the summer solstice was in the 9th 
degree of Leo; now, it appears from above, that .^irius rises heliacaiiy 
at Alexandria, when the sun is in the 12th degree of IjCo ; and, as a de¬ 
gree nearly answers to a day Sirius rose heliacaiiy, in the time of Hesi¬ 
od, about four days after the summer solstice ; and, if the Dog Days 
continued forty days, they ended about forty-four days after the sum¬ 
mer solstice. The Dog Days, in our almanacs begin on the third of 
July, which is twelve days after the summer solstice, and end on the 
eleventh of August, which is fifty-one days after the summer solstice ; 
and their continuance is thirty-nine days Hence, it is plain, that the 
Dog Days of the moderns have no reference whatever to the rising of 
Sirius, for this star ri.ses heliacaiiy at London on the twenty-fifth of 
August, and, as well as the rest of the stars, varies in its rising and set¬ 
ting, according to the variation of the latitudes of places, and, there¬ 
fore, it could have no influence whatever on the temperature of the at¬ 
mosphere ; yet, as the Dog Star rose heliacaiiy at the commencement of 
the hottest season in Egypt, Greece, &c. in the earlier ages of the 
world, it was very natural for the ancients to imagine that the heat, 
&c. was the effect of this star. A few years ago, the Dog Day s in our 
almanacs began at the cosmical rising of Procyon viz. on the SOth of 
July, and continued to the 7th of September ; but they are now, very 
properly altered, and made not to depend on the variable rising of any 
particular star, but on the summer solstice^ 



276 


rriOBLEMS PERFORMED BY 


5, At what lime of the year does Procyon rise ami 
Bet heliacally at London ? 

6. If the precession of the equinoxes be 50i seconds 
in a year, how many years will elapse, from 1808, before 
Sirius the Dog Star, will rise heliacally at Christmas, at 
Cairo in Egypt ? When this period happens, Sirius 
will perhaps no longer be accused of bringing sultry 
weather. 


PROBLEM LXXVI. 

The latitude of a 'place, and day of the month being 
given, to find all those stars that rise and set acrony- 
cally, cosmically, and heliacally.^ 

Rule. Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the given place. 
Then, 

1. For the acronycal rising and setting) find the 
sun’s place in the ecliptic, and bring it to the w^estern 
edge of the horizon, and all the stars along the eastern 
edge of the horizon will rise acronycally, while those 
along the western edge will set acronycally. 

2. For the cosmical rising and setting, bring the 
sun’s place to the eastern edge of the horizon, and all 
the stars along that edge of the horizon will rise cosmi- 


* This problem is the reverse of the three preceding problems. Their 
principal use is to illustrate several passages in the ancient writers, 
such as Hesiod, Virgil, Columella, Ovid, Pliny, &c. See Definition 
6A, page 14. The knowledge of these poetical risings and settings 
of the stars was held in great esteem amone the ancients, and was very 
useful to them in adjusting the times set apart for their religious and 
civil duties, and for marking the seasons proper for the several parts of 
husbandry ; for the knowledge which the ancients had of the motions 
of the heavenly bodies was not sufficient to adjust the true length of the 
year ; and, as the returns of the seasons depend upon the approach of 
the sun to the tropical and equinoctial points, so they made use of these 
risings and settings to determine the commencement of the different sea¬ 
sons, the time of the overflowing of the Nile, &c. The knowledge 
which the moderns have acquired of the motions of the heavenly bodies 
renders such observations as the ancients attended to in a great measure 
useless, and, instead of watching the rising and setting of particular 
stars for any remarkable season, they can sit by the fire-side and consult 
an almanac. 



THE CELESTIAL GLOBE. 277 

cally, while those along the western edge will set cosmi- 
caliy. 

3 . For the heliacal rising and settingy screw the 
quadrant of altitude over the latitude, turn the globe 
eastward on its axis till the sun’s place cuts the quad¬ 
rant twelve degrees below the horizon, then all stars of 
the first magnitude, along the eastern edge of the hori¬ 
zon, will rise heliacallj ; and, by continuing the motion 
of the globe eastward till the sun’s place intersects the 
quadrant in 13, 14, 15, &c. degrees below the horizon, 
you will find all the stars of the second, third, fourth, &c. 
magnitudes, which rise heliacally on that day. By 
turning the globe westward on its axis, in a similar man¬ 
ner, and bringing the quadrant to the western edge of 
the horizon, you will find all the stars that set heliacally. 

Examples, 1. What stars rise and set cosmically at 
Edinburgh, on the 11th of June? 

Answer. The bright star in Castor, Aldebaran in Taurus, Foraal- 
baut in the Southern Fish, &;c. rise cosmically ; those stars in the body 
of Leo Minor, the arm of Virgo, the right foot of Bootes, part of the 
Centaur, &c. set cosmically, 

2 . What stars rise and set acronycally at Drontheim 
in Norway, latitude 63° 26' N. on the 18th of May ? 

Answer. Altair in the Eagle, the head of the Dolphin, &c. rise a- 
cronycally ; and Aldebaran in Taurus, Betelguese in Orion, &c. set a- 
cronycally. 

3. What star of the first magnitude rises heliacally at 
London, on the 7th of October ? 

Answer. Arcturus in Bootes. 

4. What star of the first magnitude sets heliacally at 
London, on the 5th of May ? 

Answer. Sirius the Dog Star. 

5 . What stars rise and set acronycally at London, on 
the 26th of September ? 

6 . What stars rise and set cosmically at Lotidon, on 
the 23d of March ? 

PROBLEM LXXVII. 

To illustrate the precession of the equinoxes. 

Observations, All the stars in the different constel¬ 
lations continually increase in longitude ; consequently, 
either the whole starry heavens have a slow motion 
from west to east, or the equinoctial points have a slow 


278 


PROBLEMS PERFORMED BY 


motion from east to west. In the time of Meton,^ the 
first star in the constellation Aries, now marked /3, pas¬ 
sed through the vernal equmox, whereas it is now up¬ 
wards of 30f degrees to the eastward of it. 

Illustration* Elevate the north pole 90 degrees a- 
bove the horizon, then will the eqiiinociiai coincide with 
the horizon ; bring the polej of the ecliptic to that part 
of the brass meridian which is numbered from the north 
pole towards the equinoctial, and make a mark upon the 
brass meridian above it; let this mark be considered as 
(he pole of the world, let the equinoctial represent the 
ecliptic, and let the ecliptic be considered as the equi¬ 
noctial ; then count 38^ degrees, the complement of the 
latitude of London, from this pole upwaids, and mark 
where the reckoning ends, which will be at 75 degrees, 
on the brass meridian, from the southern point of the 
horizon , this mark will stand over the latitude of Lon¬ 
don. 

Now turn the globe gently on its axis, from east to 
west, and the equinoctial points w ill move the same way, 
while, at the same lime, the pole of the world|| will de¬ 
scribe a circle round the pole of the ecliptic^ of 46° 56' 
in diameter; this circle will be completed in a PlatonicTT 
year, consisting of 25,791 years, at the rate of 50L sec¬ 
onds in a year, and the pole of the heavens will vary its 


* Melon was a famous mathematician of Athens, who flourished 
about 430 years before Christ. In a book called Enneatlecaterides, or 
cycle of 19 years, he endeavoured to adjust the course of the sun and of 
the moon , and attempted to show that the solar and lunar years could 
regularly begin from the same point in the heavens. 

t If the precession of the equinoxes be 50^'' in a year, and if the equi¬ 
noctial colure passed through Arietis, 430 years before Christ, the 
longitude of this star oue:ht now (1804) to be 31® 10' 58", fori year; 
50i" : : 2234 years (=430 X 1804) : 31° 10' 58", and this longitude is 
not far from the truth. 

If The pole of the ecliptic is that point on the globe, in the arctic 
circle, where the circular lines meet. 

j| Let it be remembered that the pole of the ecliptic on the globe here 
represents the pole of the world. 

0 Take notice, that the extremity of the globe^s axis here represents-' 
the pole of the ecliptic. 

IT A platonic year is a period of time determined by the >revolution 
of the equinoxes : this period being once completed, the ancients were 
of opinion that the world was to begin anew, and the same series of 
things to return over again. See the 64th Definition, page 14* 



the celestial globe. 


279 


situation a small matter every year. When 12,895-^- 
years, being halt of a Plaioiiic year, are completed (which 
may be known by turning the globe half round, or till the 
point Aneis coincides with the eastern point of the hori¬ 
zon,) that point ot the heavens which is now 8^ degrees 
souin of the zenith of London will be the north pole, as 
may be seen by referring to the mark which was made 
over 75 degrees on the meridian. 

PROBLEM LXXVIII. 

To find the distances of the stars from each other in de¬ 
grees. 

Rule, Lay the quadrant of altitude over any two 
stars, so that the division marked O may be one of the 
stars ; the degrees between them will show their dis¬ 
tance, or the angle which these stars subtend, as seen by 
a spectator on the earth. 

Examples, 1. What is the distance between Vega 
in Lyra, and Altair in the Eagle? 

Answer. 34 Degrees. 

2. Required the distance between jS in the Bull’s 
Horn, and y Bellatrix in Orion’s shoulder. 

3. What is the distance between /S in Pollux and<6 in 
Procyon ? 

4. What is the distance between Hy the brightest of 
the Pieaides, and /Sin the Great Dog’s Foot ? 

5. What is (he distance between e in Orion’s girdle, 
and ^in Cetus ? 

6. What is the distance between Arcturus in Bootes,^ 
and /S in the right shoulder of Serpentarius ? 


PROBLEM LXXIX. 

To find what stars lie in or near the moon's path, or 
what stars the moon can eclipse, or make a near ap¬ 
proach to. 

Rule, Find the moon’s lonffitude and latitude, or her 
(ight ascension and declination, in an ephemeris, for sev- 


280 


PROBLEMS PERFORMED BY 


eral days, and mark the moon’s places on the globe (as 
directed in Problems LXVIII or LXVII ;) Oien by 
laying a thread or the quadrant of altitude, over these- 
places, you will see nearly the moon’s path,* and, conse¬ 
quently, what stars lie in her way. 

Examples, 1. What stars were in or near the moon’s 
path, on the 10th, 11th, 13th, and 16th of December, 
1805. 


10th, ®’s longitude SI 20° 12' latitude 3° 34'S. 
11th, - - tiK 4 22 - - 4 25 S. 

13th, - . -2= 1 .39 - - 5 15 S. 

16th, - - nt 10 11 - - 4 26 S. 

Answer. The stars will be found to be Cor Leonis or Regulus, Spi- 
ca Vii ginis, u in Libra, &c. See page 4T, White’s Ephemeris. 


2. On the 16th, 17th, 18th, 19tb, and 20th of May, 
1813, what stars lay near the moon’s way ? 

16th, ®’s right ascension, 252° 22', declination 18° 5' S. 
irtb, - - - 264 54 - - 19 37 S. 

18th, - - - 277 42 - .20 18 S* 

19th, - - - 290 42 - - 20 23 S. 

20th, - - - 303 47 - - 18 48 S. 


PROBLEM LXXX. 


Given the latitude of the place and the day of the month, 
tofind what planets will be above the horizon after 
sun-setting. 

Rule. Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the place; find the 
sun’s place in the ecliptic, and bring it to the western 
part of the horizon, or to ten or twelve degrees below ; 
then look in the ephemeris for that day and month, and 
you will find what planets are above the horizon, such 
planets will be fit for observation on that night. 


* The situation of the moon’s orbit for any particular day nmy be 
found thus : find the place of the moon’s ascending node in the Ephem¬ 
eris, mark that place and its antipodes (being the descending node) on 
the globe ; half the way between these points make marks 5® 20' on 
the north and south side of the ecliptic, viz. let the northern mark be 
between the ascending and descending node, and the southern between 
^ the descending and ascending node ; a thread tied round these four 
points will show the position of the moon’s orbit. 




THE CELESTIAL GLOBE. 


201 


Examples. 1. Were any of the planets visible after 
the sun had descended ten degrees* below the horizon of 
London, on the 1st of December, 1805 ? Their longi¬ 
tudes being as follows : 

5 8* 22° 30' X 8* 15** 27' #’s longitude at 

9 9 23 40 he 24 50 midnight 0* 9° 

S 8 25 21 ¥ 6 24 5 

Answer. Venus and the moon were visible. 

2. What planets will be above the horizon of London 
when the sun has descended ten degrees below, on the 
25th of January, 1813 ? Their longitudes being as fol¬ 
lows : 

5 9* 11° 22' H 4s 3*^ 53' •’s longitude at 

$ 9 5 30 >2 9 13 14 midnight 7* 21° 47' 

^ 7 29 18 7 27 14 

PROBLEM LXXXI. 

Given the latitude of the place^ day of the month, and 
hour of the night or morning, to find what planets 
will be visible at that hour. 

Rule. Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the place ; find 
the sun’s place in the ecliptic, bring it to the brass meri¬ 
dian, and set the index of the hour circle to 12 ; then, 
if the given time be before noon, turn the globe east¬ 
ward till the index has passed over as many hours as 
the time wants of noon ; but, if the given time be past 
noon, turn the globe westward on its axis till the index has 
passed over as many hours as the time is past noon; let 
the globe rest in this position, and look in the Epheme- 
ris for the longitudesf of the planets, and, if any of them 


* The planets are not visible till the sun is a certain number of de¬ 
grees below the horizon: and these degrees are variable according to the 
brightness of the planets. Mercury becomes visible when the sun is 
about 10 deg. below the horizon ; Venus when the sun^s depression is 
5 deg.; Mars 11® SO' ; Jupiter 10°; Saturn ll« ; and the Georgian 
17® SO'. 

t It is not necessary to give the latitudes of the planets in this prob¬ 
lem; for, if the signs and degrees of the ecliptic in which their longi¬ 
tudes are situated above the horizon, the planets will likewise be above 
the horizon. 





282 


PROBLEMS PERFORMED BY 


be in the signs which are above the horizon, such plan¬ 
ets will be visible. 

Examples. 1. On the first of December, 1805, the 
longitudes of the planets, by an ephemeris, were as fol¬ 
lows ; were any of them visible ai London at five o’clock 
in the morning ? 

5 8* 22** 30' “U 8* 15® 27' #’s longitude at 

5 0 23 40 h 6 24 50 midnight 0'9° 15'. 

^ 8 25 21 6 24 5 

Answer. Saturn and the Oeorgiura Sidus were visible, and both near¬ 
ly in the same point of the heavens, near the eastern horizon; Satarn 
was a little to the north of the Georgian. 

2. On the first of October, 1813, the longitudes of the 
planets in the fourth page of the Nauiical Almanac, were 
as follows : were any of them visible at London at ten 
o’clock in the evening ? 

5 6* 1° 26' H 5’ 0° 23' #’8 longitude at 

$ 7 11 43 >2 9 12 55 midnight 9s 0° 42' 

^ 10 8 29 ¥ 7 25 23 

PROBLEM LXXXII. 

The latitude of the place and day of the month giveUy to 

find how long Venus rises before the sun, when she is 
a morning star, and how long she sets after the sun, 
when she is an evening star. 

Rule. Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the place ; find 
the latitude and longitude of Yenus in an ephemeris, and 
mark her place on the globe; find the sun’s place in the 
ecliptic, and bring it to the brass meridian ; then, if the 
place of Venus be to the right hand of the meridian, she 
is an evening star ; if to the left hand, she is a morning 
star. 

When Venus is an evening star. Bring the sun’s 
place to the western edge of the horizon, and set the in¬ 
dex of the hour circle to 12 ; turn the globe westward on 
its axis till Venus coincides with the western edge of 
the horizon; and the hours passed over by the index 
will show how long Venus sets after the sun. 

When Venus is a morning star. Bring the sun’s 
place to the eastern edge of the horizon, and set the in¬ 
dex of the hour circle to 12 ; turn the globe eastward on 


THE CELESTI4L GLOBE. 


283 


its axis till Venus comes to the eastern edge of the ho¬ 
rizon, and tbe hours passed over by the index will show 
how long Venus rises before the sun. 

Note. 2 he same rule will servefor Jupiter^ hy mark¬ 
ing his place instead of that of Venus, 

Examples. 1. On the tirst of March, 1805, the lon¬ 
gitude of Venus was 10 signs 18 deg. 14 min. or 18 deg. 
14 min. in Aquarius, latitude 0 deg. 52 min. south ; 
was she a raor- ng or an evening star ? If a morning 
star, how long did she rise before the sun at London ? If 
an evening star, how long did she shine after the sun 
set ? 

Answer. Venus was a morning star, and rose three quarters of an 
hour before the sun. 

2. On the 25th of October, 1805, the longitude of Ju¬ 
piter was 3 signs 7 deg. 27 min. or 7 deg. 27 min. in 
Sagittarius, latitude 0 deg. 29 min. north ; was 
he a morning or an evening star? If a morning star, 
how long did he rise before the sun at London ? If an 
€vening star, how long did he shine after the sun set ? 

Answer. Jupiter was an evening star, and set 1 hour and 20 minutes 
after tbe sun. 

3. On the first of November, 1813, the longitude of 
Venus was 8 signs 18 deg. 50 min. latitude 2 degrees 3 
min. south ; was she a morning or an evening star ? 
If she were a morning star, how long did she rise before 
the sun at London ? If an evening star, how long did 
she shine after the sun set ? 

4. On the seventh of January, 1813, the longitude of 
Jupiter was 5 signs 6 deg. 36 min. latitude 0 deg. 56 
min. north, was he a morning or an evening star ? 
II he were a morning star, how long did he rise before the 
sun ? If an evening star, how long did he shine after the 
sun set ? 


284 


PROBLEMS PERFORMED BY 


PROBLEM LXXXIH. 


The latitude of a place and day of the month^ being 
givetif to find the meridian altitude of any star or 
planet* 


Rule, Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the given place: 
theii) 

For a star. Bring the given star to that part of the 
brass meridian which is numbered from the equinoctial 
towards the poles ; the degrees on the meridian, contain¬ 
ed between the star and the horizon, will be the altitude 
required. 

jPor the moon or a planet. Look in an ephemeris for 
the planet’s latitude and longitude, or for its right ascen¬ 
sion and declination, for the given month and day, and 
mark its place on the globe (as in Prob. LXVIII or 
LXVII ;) bring the planets place to the brass meridian; 
and the number of degrees between that place and the 
horizon will be the altitude. 

Examples, 1. What is the meridian altitude of AI- 
debarau in Taurus at London ? 

Answer. 54° S6'. 

2. What is the meridian altitude of Arcturus in Bootes, 
at London ? 

3. On the first of September, 1813, the longitude of 
Mars was 10 signs 2 deg. 20 min. and latitude 5 
deg. 48 min. south ; what was his meridian altitude at 
London ? 

4. On the first of April, 1813, the longitude of Saturn 
was 9 signs 18 deg. 47 min. and latitude 0 deg. 
23 min. north ; what was his meridian altitude at Lon¬ 
don ? 

5. On the eleventh of April, 1805, at the time of the 
moon’s passage over the meridian of Greenwich, her 


* The meridian altitude of the stars on the globe, in the same lati¬ 
tude, are invariable ; therefore, when the meridian altitude of a star is 
paught, the day of the month need not be attended to. 




THE CELESTIAL GLOBE. 


28 ^ 


right ascension was 208 deg. 7 min.* and declination 16 
deg. 48 min. south; required her meridian altitude at 
Greenwich.f 
Answer. 21® 42'. 


PROBLEM LXXXIV. 

To find all those places on the earth to which the moon 
will be nearly vertical on any given day. 

Rule, Look in an ephemeris for the moon’s latitude 
and longitude for the given day, and mark her place on 
the globe (as in Prob. LXVIll.) bring this place to that 
part of the brass meridian which is numbered from the 
equinoctial towards the poles, and observe the degree 
above it; for all places on the earth having that latitude 
will have the moon vertical (or nearly so) when she comes 
to their respective meridian's. 

Or ; take the moon’s declination from page VI. of the 
Nautical Almanac, and mark whether it be north or 
south ; then, by the terrestrial globe, or by a map, find 
all places having the same number of degrees of latitude 
as are contained in the moon’s declination, and those will 
be the places to which the moon will be successively 


* By the Nautical Almanac, the moon passed over the meridian at 40 
minutes past ten o’clock in the evening, on the llth of April 1805. 

208® 48' ^’s right ascension at midnight.—-Declination IT® S' S. 
. 202 47 do. at . - - noon - do. 14 56 S. 


6 4 increase in 12 hours from noon 

12 h.: 6® 1' :: 10 h. 40' : 5® 20'; li h.: 2® 7' 
hence, 202® 47'-f 5° 20'=208® 7' 
the moon’s right ascension at 40 
minutes past 10. 


2 7 

10 h. 40 ': 1® 52'; 
hence, 14® 56' -f-1® 52'=16° 48' 
the moon’s declination at 40 min. 
past 10. 


The places of the planets may be taken out of the ephemeris for noon 
without sensible error, because their declinations vary less than that of 
the moon. 

t The moon will have the greatest and least meridian altitude to all 
the inhabitants north ©f the equator, when her ascending node is in 
Aries; for her orbit making an angle of 51° with the ecliptic, her great¬ 
est altitude will be 5l° more than the greatest meridional altitude of the 

sun, and her least meridional altitude 51® less than that of the sun. 

3 ^ 

The greatest altitude of the sun at London iS 62® ; the moon’s greatest 
altitude is therefore 67® 20'. The least meridional altitude of the sun 
at London is 15°; the least meridional altitude of the moon is therefore 
9® 40'. 





286 


PROBLEMS PERFORMED BY 


vertical on the given day. If the moon’s declination be 
north, the places will be in north latitude ; if the 
moon’s declination be south, they will be in south lati¬ 
tude. 

Examples, 1. On the 15th of October, 1805, the 
moon’s longitude at midnight was 3 signs 29 deg. 14 
min. and her latitude 1 deg. 35 min. south ; over what 
places did she pass nearly vertical I 

Answer. From the moon^s lat’tmie and longitude being given, her 
declination may be found by the globe to be about 19® north. The 
moon was vertical at Porto Kico, St. Domingo, the north of Jamaica, 
O’why’hee, &c. 

2. On the 20th of December, 1813, the moon’s lon¬ 
gitude at midnight was 8 signs 9 deg. and her latitude 4 
deg. 7 min. north; over what places on the earth did 
she pass nearly vertical ? 

3. What is the greatest norih declination which the 
moon can possibly have, and to what places will she be 
then vertical ? 

4. What is the greatest south declination which the 

moon can possibly have, and to what places will she be 
then vertical ? ^ 

PROBLEM LXXXV. 

Given the latitude of aplace, day of the mouthy and the 
altitude of a star, to find the hour of the nighty and 
the starts asimuth. 

Rule. Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the place, and 
screw the quadrant of altitude upon'the brass meridian 
over that lalitude ; find the sun’s place in the ecliptic, 
bring it to the brass meridian, and set the index of the 
hour circle to 12; bring the lower end of the quadrant 
of altitude to that side of the meridian* on which the 
star was situated when observed ; turn the globe west- 


* It is necessary to know on which side of the meridian the star is 
at the time of observation, because it will have the same altitude on 
both sides of it. Any star may be taken at pleasure, but it is best to 
take one not too near the meridian, because for some time before the 
star comes to the meridian, and after it has passed it, the altitude varies 
very little. 



THE CELESTIAL GLOBE. 


287 


ward till the centre of the star cuts the given altitude on 
the quadrant; count the hours which the index has passed 
over, and they wdl show the time from noon when the 
star has the given altitude : the quadrant will intersect 
the horizon in the required azimuth. 

Examples. 1. At London, on the 281h of December, 
the star Deneb in the Lion’s tail, marked /3, was observ¬ 
ed to be 40 deg. above the horizon, and east of the 
meridian, what hour was it, and what was the star’s azir 
muth ? 

Answer. By bringing the fiun’s place to the meridian, and turning 
the gh>be wes^tward on its axis till the star cuts 40 deg. of the quadrant 
east of the meridian, the index will have passed over 14 hours; conse¬ 
quently the ^tar has^, 40 deg. of altitude east of the meridian, 14 hours 
from noon, or at two o’ch ek in »he morning. Its azimuth will be 62^ 
deg from the south towards the east. 

2. A? London on ihe 28 of December, the starin 
the Lion’s tail, was observed to be westward of the me¬ 
ridian, and to have 40 deg. of altitude ; what hour was it, 
and what was the star’s azimuth ? 

Answer. By turning the globe westward on its axis till the star 
cuts 40 deg. of the quadrant, west of the meridian, the index w ill have 
passed over 20 hours ; consequently, the star has 40 deg. of altitude 
west of the meridian 20 hours from noon, or eight o’clock in the morn¬ 
ing Its azimuth will be b2^ deg. from the south towards the west. 

3. At London, on the 1st of September, the altitude 
of Benetnach in Ursa Major, marked Uy was observed (o 
be 36 deg. above the horizon, and west of the meridian, 
what hour was it, and what was the star’s azimuth ? 

4. On the 21st of December, the altitude of Sirius, 
when west of the meridian at London, was observed to 
be 8 deg. above the horizon ; what hour was it, and 
what was the star’s azimuth ? 

5. On the 12th of August, Menkar in the Whale’s 
Jaw, marked was observed to be 37 deg. above the 
horizon of London, and eastward of the meridian ; what 
hour was it, and what was the star’s azimuth I 

PROBLEM LXXXVI. 

Given the latitude of a place, day of the month, and 

hour of the day, to find ihe attitude of any star, and 

its azimuth. 

Rule. Elevate the pole so many degrees above Ihe 
horizon are equal to the latitude of the place, and 


288 


PROBLEMS PERFORMED BY 


screw the quadrant of altitude upon the brass meridian 
over that latitude ; find the sun’s place in the ecliptic, 
bring it to the brass meridian, and set the index of the 
hour circle to 12; then, if the given time be before noon, 
turn the globe eastward on its axis till the index has 
passed over as many hours as the time wants of noon ; if 
the time be past noon, turn the globe westward till the 
index has passed over as many hours as the time is past 
noon : let the globe rest in this position, and move the 
quadrant of altitude till its graduated edge coincides 
with the centre of the given star; the degrees on the 
quadrant, from the horizon to the star, will be the alti¬ 
tude ; and the distance from the north or south point of 
the horizon to the quadrant, counted on the horizon, will 
be the azimuth from the north or south. 

Examples, 1. What are the altitude and azimuth of 
Capella, at Rome, when it is five o’clock in the morning, 
on the second of December ? 

Answer. The Altitude is 41 deg. 58 min. and the azimuth 60 deg. 
50 min. from the north towards the west. 

2. Required the altitude and azimuth of Altair in 
Aquila on the sixth of October, at nine o’clock in the 
evening, at London. 

3. On what point of the compass does the star Alde- 
baran bear at the Cape of Good Hope, on the fifth of 
March, at a quarter past eight o’clock in the evening ; 
and what is its altitude ? 

Answer. The Azimuth is 49 deg. 52 min. from the north, and its alti¬ 
tude is 22 deg. SO min. 

4. Required the altitude and azimuth of Acyone in 
the Pleiades, marked «, on the 21st of December, at four 
o’clock in the morning at London ? 

PROBLEM LXXXVII. 

Given the latitude of a place, day of the month, and 

asimuth of a star, to find the hour of the n ight and 

the starts altitude. 

Rule, Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the place, and 
screw the quadrant of altitude upon the brass meridian 
over that latitude; find the sun’s place in the ecliptic, 


tHE CELESTIAL GLOBE, 


289 


bring it to the brass meridian, and set the index of the 
hour circle to 12 ; bring the lower end of the quadrant 
of altitude to coincide with the given azimuth on the 
horizon, and hold it in that position ; turn the globe 
westward till the given star comes to the graduated edge 
of the quadrant, and the hours passed over by the index 
will be the time from noon, the degrees on the quadrant, 
reckoning from the horizon to the star, will be the alti¬ 
tude. 

Examples. 1. At London, on the 28ih of December, 
the azimuth of Deneb in the Lion’s tail, marked /3, was 
62|^ deg. from the south towards the west; what hour 
was it, and what was the star’s altitude ? 

Answer. By turning the globe westward on its axis the index will 
passover20 hours before the star intersects the quadrant; therefore, 
the time will be 20 hours from noon, or eight o’clock in the morning ; 
and the star’s altitude will be 40 deg. 

2. At London, on the 5ih of May, the azimuth of Cor 
Leonis, or Regulus, marked was 74 deg. from the 
south towards the west; required the star’s altitude, and 
the hour of the night. 

3. On the 8th of October, the azimuth of the star 
marked jS, in the shoulder of Auriga, was 50 deg. from 
the north towards the east; required its altitude at Lon¬ 
don, and the hour of the night. 

4. On the 10th of September, the azimuth of the star 
marked e in the Dolphin, was 20 deg. from the south to¬ 
wards the east ; required its altitude at London, and 
the hour of the night. 

PROBLEM LXXXVIII. 

Trvo stars being given^ the one on the meridian, and 

the other on the east or west point of the horizon, to 

find the latitude of the place. 

Rule. Bring the star which was observed to be on 
the meridian, to the brass meridian ; keep the globe 
from turning on its axis, and elevate or depress the pole 
till the other star comes to the eastern or western part of 
the horizon ; then the degrees from the elevated pole to 
the horizon will be the latitude. 

39 


290 


PROBLEMS PERFORMED BY 


Examples, 1. When the two pointers* of the Great 
Bear, marked <* and /3, or Dubhe and (i, were on the me¬ 
ridian, I observed Vega in Lyra to be rising ; required 
the latitude. 

Answer. 27 deg. north. 

2. When Arclurusin Bootes was on the meridian, Altair 
in the Eagle was rising; required the latitude. 

3. When the star marked /Sin Gemini was on the meri¬ 
dian, e in the shoulder of Andromeda was setting; re¬ 
quired the latitude. 

4. In what latitude are <«and /3, or Sirius and in 
Canis Major rising, when Algenib, or«, in Perseus, is on 
the meridian ? 


PROBLEM LXXXIX. 

The latitude of the placet Ihe day of the monthy and 
two stars that have the same asimuthi-\ being giveiiy 
to find the hour of the night. 

Rule, Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the place, and 
screw the quadrant of altitude upon Ihe brass meridian 
over that latitude : find the sun’s place in the ecliptic, 
bring it to the brass meridian, and set the index of the 
hour circle to 12 ; turn the globe on its axis from east 
to west till the two given stars coincide with the gradua¬ 
ted edge of the quadrant of altitude ; the hours passed 
over by the index will show the time from noon ; and 
the common azimuth of the two stars will be found on 
the horizon. 


* These two stars are called the pointers, because a line drawn 
through thetP, points to the polar star in Ursa Minor. 

t To find what stars have the same azimuth —Let a smooth rectan¬ 
gular board of about a foot in breadth, and Three feet high (or of any 
height you please,) be fixed perpendicularly upon a stand ; draw a 
straight line through the middle of the board, parallel to the sides ; fix 
a pin m the upper part of this line, and make a hole in the board at the 
lower part of the line ; hang a thread with a plummet fixed to it. upon 
the pin, and let the ball of the plummet move freely in the hole made in 
the lower part of the board t set this board upon a table in a window, 
or in the open air, and wait till the plummet ceat.es to vibrate ; then 
look along the face of the board, and those stars which are parUy hid 
from your view by the thread, will have the same azimuth. 



THE CELESTIAL GLOBE. 


291 


Examples. 1. At what hour, at London, on the 
first of May, will Altair in the Eagle, and Vega in the 
Harp, have the same azimuth, and what will that azi¬ 
muth be ? 

Answer. By bringing the sun’s place to the meridian, &c. and turn¬ 
ing the globe westward, the index will pass over 15 hours before the 
stars coincide with the quadrant: hence, they will have the same azi¬ 
muth at 15 hours from noon, or at three o’clock in the morning ; and 
the azimuth will be 42^ degrees from the south low'ards the east. 

2. On the 10th of September, what is the hour at 
London when Deneb in Cygnus, and Markab in Pegasus, 
have the same azimuth, and what is the azimuth ? 

3. At what hour on the 15th of April will Arcturus 
and Spica Virginis have the same azimuth at London, 
and what will that azimuth be ? 

4. On the 20th of February, what is the hour at 
Edinburgh when Capella and the Pleiades have the same 
azimuth, and what is the azimuth ? 

5. On the 21st of December, what is the hour at 
Dublin when or Algenib in Perseus, and ^ in the 
Bull’s Horn, have the same azimuth, and what is the 
azimuth ? 


PROBLEM XC. 

The latitude of a place, the day of the month, and two 

stars, that have the same altitude, being given, to 
find the hour of the night. 

Rule. Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the place, and 
screw the quadrant of altitude upon the brass meridian 
over that latitude ; find the sun’s place in the ecliptic, 
bring it to the brass meridian, and set the index of the 
hour circle to 12 ; turn the globe on its axis from east 
to west till the two given stars coincide with the given 
altitude on the graduated edge of the quadrant ; the 
hours passed over by the index will be the time from 
noon when the two stars have that altitude. 

Examples. T. At what hour at London, on the sec¬ 
ond of September, will Markab in Pegasus, and a, in the 
head of Andromeda, have each 30 deg. of altitude ? 
Answer. At a quarter past eight in the evening. 

2, At what hour at London, on the fifth of January, 


292 


PROBLEMS PERFORMED BY 


willa, Menkar in the Whale’s jaw, and Aldebaran 
in Taurus; have each 35 deg. of altitude ? 

3. At what hour at Edinburgh, on the tenth of No¬ 
vember, will <«, Altair in the body of the Eagle, and 
in the tail of the Eagle, have each 35 deg. of altitude ? 

4. At what hour at Dublin, on the 15(h of May, will v, 
Benetnach in the Great Bear’s tail, and y, in the shoul¬ 
der of Bootes, have each 56 deg. of altitude^? 

PROBLEM XCI. 

The altitudes of two stars having the same azimuth, 

and that azimuth being given, to find the latitude of 

the place* 

Rule. Place llie graduated edge of the quadrant of 
altitude over the two stars, so that each star may be ex¬ 
actly under its given altitude on the quadrant ; hold the 
quadrant in this position, and elevate or depress the pole 
till the division marked O, on the lower end of the quad¬ 
rant, coincides with the given azimuth on the horizon ; 
when this is effected, the elevation of the pole will be 
the latitude. 

Examples. 1. The altitude of Arcturus was ob¬ 
served to be 40 deg. and that of Cor Caroli 68 deg. ; 
their common azimuth at the same time was fl deg. 
from the south towards the east ; required the latitude. 

Answer. 51^ deg. north. 

2. The altitude of t in Castor was observed to be 40 
deg. and that of /S in Procyon 20 deg. ; their common 
azimuth at the same time was 73^ deg. from the south 
towards the east ; required the latitude ? 

3. The altitude of u, Dubhe, was observed to be 40 
deg. and that of yin the back of the Great Bear 29^ 
deg. ; their common azimuth at the same time was 30 
deg. from the north towards the east; required the 
latitude. 

4. The latitude of Vega, or «, in Lyra was observ¬ 
ed to be 70 deg. and that of«« in the head of Hercules 

deg. ; their common azimuth at the same time was 
60 deg. from the south towards the west; required the 
latitude. 


THE CELESTIAL GLOBE. 




PROBLEM XCII. 

The day of the month being given, and the hour when 
any known star rises or sets, to find the latitude of 
the place. 

Rule. Find the sun’s place in the ecliptic, bring it 
to the brass meridian, and set the index of the hour cir¬ 
cle to 12 ; then, if the given time be before noon, turn 
the globe eastward till the index has passed over as ma¬ 
ny hours as the time wants of noon : but, if the given 
time be past noon, turn the globe westward till the index 
has passed over as many hours as the time is past noon; 
elevate or depress the pole till the centre of the given 
star coincides with the horizon; then the elevation of 
the pole will show the latitude. 

Examples. 1. In what latitude does e Mirach, in 
Bootes rise at half past twelve o’clock at night, on the 
tenth of December ? 

Answer. 51^ degrees north. 

2. In what latitude does Cor Leonis, or Regulus, 
rise at ten o’clock at night, on the twenty-6rst of Jan¬ 
uary ? 

3. In what latitude does Rigel in Orion, set at 
four o’clock in the morning, on the twenty-first of De¬ 
cember ? 

4. In what latitude does /3, Capricornus, set at eleven 
o’clock at night, on the tenth of October ? 


PROBLEM XCm. 

To find on what day of the year any given star passes 
the meridian at any given hour. 

Rule. Bring the given star to the brass meridian, 
and set the index to 12 ; then, if the given time be be¬ 
fore noon,* turn the globe westward till the index has 


* If the given star comes to the meridian at noon, the sun’s place 
will be found under the brass meridian, without turning the globe } if 




294 


PROBLEMS PERFORMED BY 


E assed over as many hours as the time wants of noon ; 

ut, if the given time be past noon, turn the globe east¬ 
ward till the index has passed over as many hours as 
the time is past noon; observe that degree of the eclip¬ 
tic which is intersected by the graduated edge of the 
brass meridian, and the day of the month answering 
thereto, on the horizon, will be the day required. 

Examples. 1. On what day of the month does Pro- 
cyon come to the meridian of London at three o’clock 
in the morning ? 

Answer Here the time is nine hours before noon : the globe must, 
therefore, be turned nine hours towards the west, the point of the 
ecliptic intersected by the brass meridian will then be the 9th of f , 
answering nearly to the first of December. 

2. On what day of the month and in what month, 
does «, Alderamin, in Cepheus, come to the meridian 
of Edinburgh at ten o’clock at night ? 

Answer. Here the time is ten hours after noon, the globe must, 
therefore, he turned ten hours towards the east, the point of the eclip¬ 
tic intersected by the brass meridian will then be the 17th of inj, an¬ 
swering to the ninth of September. 

3. On what day of the month, and in what month, does 
Deneb in the Lion’s tail, come to the meridian of 
Dublin at nine o’clock at night? 

4. On what day of the month, and in what month, 
does Arcturus in Bootes come to the meridian of Lon¬ 
don at noon ? 

5. On what day of the month, and in what month, 
does ^in the Great Bear come to the meridian of Lon¬ 
don at midnight ? 

6. On what day of the month, and in what month, 
does Aldebaran come to the meridian of Philadelphia, 
at five o’clock in the morning at London ? 


the given star comes to the meridian at midnight, the globe may be 
turned either eastward or westward till the index has passed ov^r 
twelve hours. 




the celestial globe. 


295 


PROBLEM XCIV. 


The day of the month being given^ to find at what houp 
any given star comes to the meridian*'^ 


Rule, Find the sun’s place in the ecliptic, bring it to 
the brass meridian, and set the index of the hour circle 
to 12; turn the globe westward on its axis till the given 
star comes to the brass meridian, and the hours passed 
over by the index will be the time from noon when the 
star culminates. 

Examples, 1, At what hour does Cor Leonis, or 
Regulus, come to the meridian of London on the twenty* 
third of September ? 

Answer. The index will pass over21| hours: hence, this star cultni* 
nates or comes to the meridian houi s after noon, or at three quar* 
ters past nine o’clock in the morning. 

2. At what hour does Arcturus come to the meridian 
of London on the ninth of February ? 

Answer. The index will pass over 16^ hours ; hence, Arcturus cul¬ 
minates 16^ hours after noon, or at half past four o’clock in the morn¬ 
ing. 

3. Required the hours at which the following stars 
come to the meridian of London on the respective days 
annexed : 


Bellatrix, January 9th. 
Menkar, May 18th. 
e Draco, Sep. 22d. 
ec Dubhe, Dec. 20th. 


jS Mirach, October 5th. 
Aldebaran, Feb. 12th. 

/S Aries, November 5th. 
e Taurus, January 24th. 


PROBLEM XCV. 

Given the azimuth of a known star, the latitude, and the 
hour, to find the star'^s altitude and the day of the 
month. 


Rule. Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the given place, 
screw the quadrant of altitude upon the brass meridian 
over that latitude, bring the division marked O, on the 
lower end of the quadrant to the given azimuth on the 


* This problem is comprehended in Problem LXXI. 




296 


PROBLEMS PEIIFORMED BY 


horizon, turn the globe till the star coincides with the 
graduated edge of the quadrant, and set the index of the 
hour circle to 12 ; then, if the given time be before noon, 
turn the globe westward till the index has passed over 
as many hours as the time wants of noon ; if the given 
time be past noon, turn the globe eastward till the index 
has passed over as many hours as the time is past noon ; 
observe that degree of the ecliptic which is intersected 
by the graduated edge of the brass meridian, and the 
day of the month answering thereto, on the horizon will 
be the day required. 

Examples. 1. At London, at ten o’clock at night, 
the azimuth of Spica Virginia was observed to be 40 
deg. from the south towards the west; required its alti¬ 
tude, and the day of the month. 

Answer. The star’s altitude is 20 deg. and the day is the 18th of 
June. The time being ten hours past noon, the globe must be turned 
ten hours towards the east. 

2. At London, at four o’clock in the morning, the azi¬ 
muth of Arcturus was 70 deg. from the south towards 
the west; required its altitude, and the day of the 
month. 

Answer. Here the time wants eight hours of noon, therefore, the 
globe must be turned eight hours westward ; the altitude of the star 
will be found to be 40 deg. and the day the l2th of April. 

3. At Edinburgh, at eleven o’clock at night, the azi¬ 
muth of cc Serpentarius, or Ras Alhagus, was 60 deg. 
from the south towards the east; required its altitude, 
and the day of the month. 

4. At Dublin, at two o’clock in the morning, the azi¬ 
muth of /S Pegasus, or Scheat, was 70 deg. from the 
north towards the east; required its altitude, and the 
day of the month. 


PROBLEM XCVI. 

The altitude of two stars being giveuy to find the lati¬ 
tude of the place. 

Rule . Subtract each star’s altitude from 00 degrees ; 
take successively the extent of the number of degrees, 
contained in each of the remainders, from the equi¬ 
noctial with a pair of compasses ; with the compasses 
thus extended, place one foot successively in the centre 
of each star, and describe arcs on the globe with a black 


THE CELESTIAL GLOBE. 


296 


lead pencil: these arcs will cross each other in the zen¬ 
ith ; bring the point of intersection to that part of the 
brass meridian which is numbered from the equinoctial 
towards the poles, and the degree above it will be the 
latitude. 

Examples, 1. At sea, in north latitude, I observed 
the altitude of Capella to be 30 deg. and that of Aldeba- 
ran 35 deg. ; what latitude was 1 in ? 

Answer. With an extent of 60 deg. (=90*—SO®) taken from the 
equinoctial, and one foot of the compasses in the centre of Capella, 
describe an arc towards the north ; then with 55 deg. (=90®—S5®,) ta¬ 
ken in a similar manner, and one foot of the compasses in the centre of 
Aldebaran, describe another arc, crossing the former; the point of in¬ 
tersection brought to the brass meridian will show the latitude to be 20^ 
deg. north. 

2* The altitude of Markab in Pegasus was 30 deg. 
and that of Altair in the Eagle, at the same time was 
65 deg. ; what was the latitude, supposing it to be 
north ? 

Answer. 29 deg. north. 

3. In north latitude the altitude of Arcturus was ob¬ 
served to be 60 deg. and that of ^ or Deneb, in the Li^ 
on’s tail, at the same time, was TO deg.; what was the 
latitude ? 

4. In north latitude, the altitude of Procyon was obser¬ 
ved to be 50 deg. and that of Betelguese in Orion, at 
the same time, was 58 deg.: required the latitude of the 
place of observation. 


PROBLEM XCVII. 

The meridian altitude of a known star being giveuy at 
anyplace in north latitude, to find that latitude. 


Rule, Bring the given star to that point of the brass 
meridian which is numbered from the equinoctial to¬ 
wards the poles ; count the number of degrees in the 
given altitude, on the brass meridian, from the star to¬ 
wards the south part of the horizon, and mark where the 
reckoning ends; elevate or depress the pole till this 
mark coincides with the south point of the horizon, and 
the elevation of the north pole above the north point of 
the horizon will show the latitude. 

40 


m 


PEOBLEMS PERFORMED B¥ 


Examples. 1. In what degree of north latitude is 
the meridian altitude of Aldebaran 52^ deg. ? 

Answer. 53 deg. 36 min. north. 

2. In what degree of north latitude is the meridian 
altitude of /J, one of the pointers in Ursa Major, 90 

• . . . j 

3. In what degree of north latitude is y, in the head 
of Draco, vertical when it culminates ? 

4. In what degree of north latitude is the meridian al¬ 
titude of e or Mirach in Bodies, 68 deg. ? 

PROBLEM XCVIII. 

The latitude of aplace, day of the month, and hour of 
the day being given, to find the Nonagesiraal Degree* 
of the[ecliptic, its altitude and azimuth, and ike Med-^ 
ium Cceli. 

Rule. Elevate the north pole to the latitude of the 
given place, and screw the quadrant of altitude upon the 
brass meridian over that latitude; find the sun’s place in 
the ecliptic, bring it to the brass meridian, and set the 
index of the hour circle to 12 ; then, if the given time be 
before noon, turn the globe eastward till the index has 
passed over as many hours as Jthe time wants of noon ; 
but, if the given time be past noon, turn the globe west¬ 
ward till the index has passed over as many hours as the 
time is past noon, and fix the globe in this position ; 
count 90 deg. upon the ecliptic from the horizon (either 
eastward or westward,) and mark where the reckoning 
ends, for that point of the ecliptic will be the nonagesi- 
mal degree, and the degree of the ecliptic cut by the 
brass meridian will be the medium cocli ; bring the 
graduated edge of the quadrant of altitude to coincide 
with the nonagesimal degree of the ecliptic thus found, 
and the number of degrees on the quadrant, counted 


* The nonagesimal degree of the ecliptic is that point which is the 
mopt elevated above the horizon, and is measured by the angle which 
the ecliptic makes with the horizon at any elevation of the pole; or, it 
is the distance between the zenith of the place and the pole of the eclip¬ 
tic. This angle is frequently used in the calculation of solar eclipses. 
The Medium Cceli, or mid-heaven, is that point of the ecliptic which is 
upon the meridian. 



THE CELESTIAL GLOBE. 


298 


from the horizon, will be the altitude of the nonagesi- 
mal degree : the azimuth will be seen on the horizon 
Note. From the 2l3t of December to the 21st of 
June, the nonagesimal degree of the ecliptic is east of 
the meridian ; and, from the 21st of June to the 21st of 
December, it is west of the meridian. 

Examples, 1. On the 21st of June, at forty-five min¬ 
utes past three o’clock in the afiernoon, at London, re¬ 
quired the point of the ecliptic which is the nonagesimal 
degree, its altitude and azimuth, the longitude of the 
medium cceli, and its altitude, &c. 

Answer. The nonagesimal degree is 10 deg. ii Leo. its altitude is 
54 deg and its azimuth 22 deg from the south towards the west, or 
nearly S. S. W. The mid-heaven, or point of the ecliptic under the 
brass meridian, is 24 deg. in Leo, and its altitude abfwe the horizon is 
52 deg. The degree of the equinoctial cut by the brass meridian, reck¬ 
oning from the point Aries, is the right ascension of the mid-heaven, 
which in this example is 146 deg. 'I he rising point of the ecliptic will 
be found to be 10 deg. in Scorpio, and the setting point 10 deg in Tau¬ 
rus. If the graduated edge of the quadrant be brought to coincide with 
the sun’s place, the sun’s altitude will be found to be 39 deg. and his azi¬ 
muth 78J deg. from the south towards the west, or nearly W. by S. 

2. At London on the 24th of April, at nine o’clock 
in the morning, required the point of the ecliptic which 
is the nonagesimal degree, its altitude and azimuth, 
the point of the ecliptic which is the mid-heaven, &c. 
&c. 

3. At Limerick, in 52 deg. 22 min. north latitude, 
on the 15th of October, at five o’clock in the afternoon, 
required the point of the ecliptic which is the nonagesi¬ 
mal degree, its altitude and azimuth, the point of the 
ecliptic which is the mid-heaven, &c. &c. 

4. At Dublin, in latitude 53 deg. 21 min. north, on 
the 15th of January, at two o’clock in the afternoon, 
required the longitude, altitude, and azimuth, of the 
nonagesimal degree ; and the longitude and altitude of 
the medium cceli. Sec, &c. 

PROBLEM XCLS:. 

The latitude of a placey day of the month, and the hotCr, 
together ivith the altitude and azimuth of a star, 
being given, to find the star. 

Ride, Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the place, and 


PROBLEMS PERFORMED BY 


iJ99 

screw the quadrant of altitude on the brass meridiaa 
over that latitude ; find the sun’s place in the ecliptic, 
bring it to the brass meridian, and set the index of the 
hour circle to 12 : then, if the given time be before 
noon, turn the globe eastward till the index has passed 
over as many hours as the time wants of noon ; but, if 
the time be past noon, turn the globe westward till the 
index has passed over as many hours as the time is past 
noon : let the globe rest in this position, and bring the 
division marked O on the quadrant to the given azimuth 
on the horizon : then, immediately under the given al¬ 
titude on the graduated edge of the quadrant, you will 
find the star. 

Examples. 1. At London on the 21st pf December, 
at four o’clock in the morning, the altitude of a star was 
50 deg. and its azimuth was 37 deg. from the south 
towards the east; required the name of the star. 

Answer. Deneb, or /3 in the Lion’s tail. 

2. The altitude of a star was 27 deg. its azimuth 76J 
deg. from the south towards the west, at eleven o’clock 
in the evening at London, on the 11th of May ; what 
star was it ? 

3. At London on the 21st of December, at four 
o’clock in the morning, the altitude of a star was eight 
deg. and its azimuth 51 deg. from the south towards 
the west ; required the name of the star. 

4. At London on the 1st of September, at nine 
o’clock in the evening, the altitude of a star was 47 deg. 
and azimuth 73 deg. from the south towards the east; 
required the name of the star. 

PROBLEM C. 

To find the time of the moon^s southing, or coming to 

the meridian of any place, on any given day of the 

month. 

Rule. Elevate the pole so many degrees above the 
horizon as are equal to the latitude of the given place; 
find the moon’s latitude and longitude, of her right as¬ 
cension and declination, from an ephemeris, and mark 
her place on the globe; bring the sun’s place to the 
brass meridian, and set the index of the hour circle to 


the celestial globe. 


300 


12 ; turn tbe globe westward till the moon’s place comes 
to the meridian, and the hours passed over by the index 
will show the time from noon, when the moon will be 
upon the meridian. 

OR, WITHOUT THE GLOBE. 

Find the moon’s place by the table, at page 244, which 
multiply by 81,* and cut off two figures from the right 
hand of the product, the left hand figures will be the 
hours ; the right hand figures must be multiplied by 60, 
for minutes. 

OR, CORRECTLY, THUS *. 

Take the difference between the sun’s and moon’s 
right ascension in 24 hours ; then, as 24 hours dimin¬ 
ished by this difference are to 24 hours, so is the moon’s 
right ascension at noon, diminished by the sun’s, to tbe 
time of the moon’s transit. 

Examples, 1. At what hour on the 12th of March, 
1805, did the moon pass over the meridian of Green¬ 
wich ? The moon’s right ascension being 136 deg. 43 
min. and her declination 14 deg. 40 min. north. 

Answer. By the Globe.—The moon came to the meridian at three 
quarters past nine in the evening.! 

By the Table, page 244,—The moon’s age is IS ; this multiplied by 
81, produces 1053, that is, 10 hours and 53 over; this 53, multiplied by 
60, produces3180, which, by rejecting the two right hand figures, leaves 
31 minutes ; so that, by this method, the moon comes to the meridian 
at 31 minutes past 10 o’clock in the evening. 

By using iht Nautical Almanac. 

Sun^s right ascension at noon 12th March=2Sh. 2S' 50" 

Ditto - - - - iSth March==23 32 SO 

Increase of motion in 24 hours - - 0 3 40 

Mood’s right ascension at noon 12th March=136® 48' 

Ditto - - - iSth March=149 4T 

Increase in 24 hours • - 12 59 equal 


* For the synodic revolution of the moon being about 29^ days, 
we have, by the rule of three, as 29^ d. : 24h : : Id. : 81h 

t The time of the moon’s rising and setting may be found as for 
a star ora planet, see Promlera LXXl; but, on account of the moon’s 
swift and irregular motion, the solution will differ materially from the 
truth. 







301 


PROBLEMS PEORFRMED BY 


to 51« 56*" ; hence, 51'56" diminished by S' 40", leaves 48' 16" life 
moon’s motion exceeds the sun’s in tk hours. 

Moon’s right ascension 186® 48' X 4=* 9'> 7' 12" 

Sun’s right ascension - - =28 28 59 

9 38 22 

24h—48' 16" : 24’' : : 9’> 38' 22" : 9^ 58' the true time of the moon’s 
passage over the meridian in the evening, agreeing exactly with the 
rfautical Almanac. 

2. At what hour, on the I5th of April, 1813, did the 
moon pass over the meridian of Greenwich? The 
moon’s right ascension being 202 deg. 40 min. and de¬ 
clination 4 deg. 35 min. south. 

3. At what hour, on the 15th of February, 1813, did 
the moon pass over the meridian at Greenwich ? The 
moon’s right ascension being 10 deg. 48 min. and de¬ 
clination 0° 13' north. 

4. At what hour on the 17th of October, 1813, did 
the moon pass over the meridian of Greenwich ? The 
moon’s right ascension being 133 deg. 44 min. and de-^ 
clination 17 deg. 46 min. north. 

PROBLEM Cl. 

The day of the months latitude of the place, and time of 
high water at the full and change of the moon being 
given, to find the time of high water on the given 
day, 

Rtile. Find the time at which the moon comes to (he 
meridian of the given place by the preceding problem, 
to which add the time of high water at the given place 
at the full and change of the moon (taken from the fol¬ 
lowing Table,) and the sum will show the time of high 
water in the afternoon. If the sum exceed 12 hours, 
subtract 12 hours and 24 minutes from it, and the remain¬ 
der will show the time of high water in the morning ; 
but, if the sum exceed 24 hours, subtract 24 hours and 
48 minutes from it, and the remainder will show the time 
of high water in the afternoon. 


• When the sun’s right ascension is greater than the moon’s, as in 
this example, 24 hours must be added to the moon’s right ascension be¬ 
fore you substract. 





IHE CELESTIAL GLOBE. 


302 


OR, BY THE TABLE, PAGE 244. 

Find the moon’s age by the Table, at page 244, and 
take out of the time from the right hand column there¬ 
of, answering to the moon’s age ; to which add the^ 
time of high water at the full and change of the moon 
(taken from the following Table,) and the sum will show- 
the time of high water in the afternoon. If the sum ex¬ 
ceed 12 hours, subtract 12 hours and 24 minutes from 
it, and the remainder will show the time of high wa¬ 
ter in the morning; but, if the sum exceed 24 hours^ 
subtract 24 hours and 48 minutes from it, and the re¬ 
mainder will show the time of high water in the after¬ 
noon. 


OR, THUS: : 

Find the time of the moon’s coming to the meridian 
of Greenwich on the given day, at page VI. of the Nau¬ 
tical Almanac : take out.the correction (from the fol¬ 
lowing Table) to correspond to this time, and apply it 
as the Table directs ; to the result add the time of high 
water at the full and change of the moon (taken from 
the following Table,) and the sum will show the time of 
high water in the afternoon. If the sum exceed 12 or 
24 hours, proceed as above. 

Examples, 1. Required the time of high water at 
London Bridge on the T2th of March 1805. The moon’s 
right ascension at that time being 136 deg. 48 min. and 
her declination 14 deg. 40 min. north. 

Answer. By the globe'—The moon came to the meridian at 9h 45' 
Time of high water at the full and change at London - 3 0 

Sum - - -' 12 45 

Subtract from it - 12 24 


Time of high water in the morning . r 0 21 

By the Table, page 244. The moon's age was IS, the time answering 
to which, in the same Table, is ... - 10*' 53' 

Time of high water at the full and change - - SO 

Sum . - - 13 53 

Subtract from it - 12 24 

1 29 


Time of high water in the morning 





.303 


PROBLEMS PERFORMED BY 


By the Nautical Almanac.—The moon came to the meridian at 9'’ 58' 
the time from the right-hand Table following answering to 9'’ 58', 


or rather 10 hours, is ----- - 

0 

r 

u 

Sum 

10 

22 

Time of high water at London at the full and change 

3 

0 

Sura 

13 

22 

Subtract from it 

- 12 

24 

Time of high water in the morning* - . - 

0 

58 


2. Required the time of high water at Hull on the 
I8th of May 1813; the moon’s right ascension being 
277 deg. 42 min. and her declination 20 deg. 18 min« 
south. 

3. Required the time of high water at Liverpool on 
the 15th of June, 1813. The moon’s right ascension 
being 287 deg. 39 min. and her declination 20 deg. 18 
min. south. 

4. Required the time of high water at Limerick on 
the 12th of August, 1813. The moon’s right ascension 
being 363 deg. 17 min. and her declination 12 deg. 59 
min. south. 

5. Required the time of high water at Bristol on the 
first of September, 1813. The moon’s right ascension 
being 237 deg. 59 min. and her declination 15 deg. 9 
min. south. 

6. Required the time of high water at Dublin, on the 
5th of December, 1813. The moon’s right ascension 
being 46 deg. 6 min. and her declination 12 deg. 13 min. 
north. 


» Here are three methods of performing the same problem, and the 
results all differ from each other : the last is the most correct: however, 
any one of these methods is as correct as those which are given in books 
on pilotage and navigation. 







the CFXESTIATi GLOBIiw 


304 


A TXBLE 

Of the time of High Water at New and Full moon 
principal places in the British Islands. 

at the 

OD 

a ^ ■ 
0 ) a 

Aberdeen 

Oh 45' 1 

Fifeness 

2h 6 ' 

■5 <» 

. ja 

Ayr 

10 30 \ 

Flamborough Head 

S 40 


Aldborough 

9 40 j 

N. and S. Foreland 

10 20 

2 .S 

St. Andrews 

2 0\ 

Fortrose 

11 40 

.2 ^ 

03 

Arran Island 

11 0 \ 

Foulness 

6 45 

^ o- 

Bam borough 

3 SO S 

Fowey 

5 40 


Banff 

0 0^ 

Galway 

3 0 

on 

u 

Beachy Head 

10 0? 

Fort George 

11 40 

S 

O 

St. Bees Head 

10 45 \ 

Fort Glasgow 

11 SO 

a 

Belfast 

10 o] 

Gravesend 

1 30 


Bembridge Point 

10 15 j 

Greenock 

11 30 

0 

•1 

Berwick 

2'SO 

Hartland Point 

4 SO 

North Berwick 

2 0 

Hartlepool 

3 0 

Jl 

2 

3 

1 

St Bride’s Bay 

6 0l 

Harwich 

11 10 

Bridlington Bay 

3 50 j 

: Holyhead 

9 45 

Bridport 

6 45 \ 

; Hull 

6 0 

n 

Brighton 

9 50 ] 

' Kinsale 

5 15 

a 

Bristol 

6 40 \ 

1 Leith 

2 20 

u 

*7 

Caithness Point 

9 Oj 

• Limerick 

4 SO 

1 

Cantire, Mall, 

10 SO i 

» Idverpool 

11 15 


Cape Clear 

4 30 \ 

1 London 

3 0 

8 

Q 

Cork 

6 SO 1 

; Milford 

5 15 

Cowes 

10 SO 

I Newcastle 

3 15 

y 

10 

11 

12 

Cromartie 

11 40 i 

1 Orfordness 

9 45 

Cormer 

7 Oj 

1 Plymouth 

6 0 

Cullen 

0 0 ■ 

> Portland 

7 SO 

Dartmouth 

6 SO ! 

> Ramsgate 

10 SO 


Dingle Bay 

3 30 ! 

1 Rochester 

0 45 

13 

Dover 

11 SO; 

1 Sandwich 

11 SO 

14 

Dublin 

9 15: 

2 Scarborough 

3 45 

Dunbar 

2 30 ' 

1 Sligo 

5 SO 

J *J 

16 

17 

Dunbarton 

11 15: 

i Southampton 

0 0 

Dundee 

2 10: 

» Stockton 

3 SO 


Dungarvon 

4 so: 

> Swansea 

6 0 

1 o 

19 

Dungeness 

9 45 

1 Tynemouth 

3 0 

Eddystone 

5 30 

1 Torbay 

6 15 


Edinburgh 

2 20 

^ Weymouth 

7 20 

20 

Exeter 

10 30 

\ Whitby 

3 20 

21 

Exmouth Bar 

6 20 

^ Whitehaven 

11 15 

Falmouth 

Fern Island 

5 30 
3 30 

1 Yarmouth 

9 0 

23 

24 






\Ad 
0 

0 2S 
0 U 

0 14 
0 0 


Sub. 
0 17 
0 34 
0 50 

I 3 
I 9 
1 3 

0 35 


Add 
0 
0 23 
0 24 
0 14 
0 0 


41 





















305 


PHOBLEMS PERFORMED BY 


PROBLEM CII. 

To describe the apparent path of any planet^ or of a 
comet, amongst the fixed stars, &c* 

Rule. Draw a straight line O, O, to represent the 
ecliptic, and divide it into any convenient number of e- 
qual parts. Set otFeight of these equal parts northward 
and southward of the ecliptic, at each end thereof: and 
draw lines as in the figure Plate V, these will represent 
the zodiac. Find the planet’s geocentric latitude and 
longitude in an ephemeris, or in the Nautical Almanac, 
and mark its place for every month, er for several days 
in each month, beginning at the right hand of the ecliptic 
line, and proceeding towards the left.* 

Find the latitudes and longitudesf of the principal 
stars in the several constellations near which the planet 
passes, and set them off in a similar manner from the 
right hand towards the left; you will thus have a com¬ 
plete picture of any part of the heavens with the posi¬ 
tions of the several stars, &c. as they appear to a spec¬ 
tator on the earth. 

Example. Delineate the path of the planet Jupiter 
for the year 1811 : the latitudes and longitudes being as 
follows : 


» The young student will recollect, that the stars appear in a con¬ 
trary order in the heavens to what they do on the surface of a globe. 
In the heavens w’e see-the concave part, on the g’obe the convex, t his 
manner of delineating the stars m-iy be found extremely useful, and will 
enable the studetit to know their names and places sooner, than by the 
globe. 

t The places of the stars may likewise be laid down by their right 
ascensions and declinations, by drawing a portion of the equinoctial 
instead of the ecliptic. 



THE TERRESTRIAL GLOBE. 


306 


Longitudes 

Latitudes. 

Longitudes. 

Latitudes. 

Jan. 1st 1*21® 45' 

0®57'S 

July 25th 2*25® 1' 

0®24' S. 

Feb. 7th 1 

22 

11 

0 

47 S. 

Aug. 7th 2 

27 36 

0 

23 S. 

--25th 1 

23 

58 

0 

43 S. 

-- 19th 2 

29 48 

0 

22 S. 

March 1st 1 

24 

20 

0 

42 S. 

-25th 3 

0 48 

0 

22 S. 

-25th 1 

28 

16 

0 

37 S. 

Sep. 7th 3 

2 45 

0 

21 S. 

April 1st 1 

29 

35 

0 

36 S. 

-25th 3 

4 50 

0 

21 S. 

-25th 2 

4 

30 

0 

32 S. 

Oct. 7th 3 

5 44 

0 

20 S. 

May 1st 2 

5 

49 

0 

31 S. 

-25th 3 

6 15 

0 

19 S. 

-13th 2 

8 

31 

0 

30 S 

Xov. 1st 3 

6 10 

0 

18 S. 

-25th 22 11 

17 

0 

29 S. 

-19th 3 

5 12 

0 

17 S. 

June 1st 2 

12 

54 

0 

28 S. 

-25th 3 

4 40 

0 

16 S. 

-25th 2 

18 

27 

0 

26 S. 

Dec. 13th 3 

2 34 

0 

U S. 

July 7th 2 

21 

49 

0 

25 S. 

-25th 3 

0 57 

0 

12 S. 


Jupiter’s path, when delineated, will be south of the 
ecliptic in the order A, B, C, D, E, F, G, H. Thus, 
he will appear at A on the 1st of January, at B on the 
1st of March, at C on the first of April, at D on the 1st 
of May, at E on the Ist of June, at F on the Tth of Ju¬ 
ly, at G on the 25th of August, and at H on the 25th of 
October. On the 25th of August, when Jupiter appears 
at G, he will be a little to the right hand of the star 
marked n in Gemini; when he arrives at H, which will 
happen on the 25th of October, he will apparently re¬ 
turn again to G, a small matter above his former path, 
where he will be situated on the 25th of December. Ju¬ 
piter will not be visible during the whole of his appar¬ 
ent progress from A to H, being too near to the sun du¬ 
ring the months of May and June. 

In the same manner the places and situations of the 
stars may be delineated; thus, Aldebaran, the principal 
star in the Hyades, will be found by the^Globe, (or a 
proper table) to be situated in 7° of EE and in 5|® of 
south latitude ; Betelguese in Orion’s right shoulder, in 
about 26® of n and in 16® of south latitude, and its place 
may be laid down on a map by extending the line of its 
longitude as from L, till it meets a straight line passing 
through 16, 16, on the sides of the map. In the same 
manner any other star’s situation may be described; 
thus, the Hyades will appear at Q, the Pleiades at P, 
&c« and Bellatrix, &c. as in the figure* 



307 


PROBLEMS PERFORMED BY 


The constellatioD Orion, here described, is a very 
conspicuous object in the heavens in the months of Jan¬ 
uary and February, about 9 or 10 o’clock in the even¬ 
ing, and will be an excellent guide for determining the 
positions of several other constellations, particularly 
Canis Major, Canis Minor, Auriga, &c. 


PART IV. 


CONTAINING, 

1. A promiscuous Collection of Examples exercising the Problems oji 
the Globes—2. A collection of Questions, with References to the 
Pages where the Answers will be found; designed as an Assistant 
to the Tutor in the examination of the Scholar..— 3. A Table of the 
Latitudes and Longitudes of the Principal Places in the World. 

CHAPTER I. 

A promiscuous Collection of Examples exercising the 
Problems on the Globes, 

1. WHAT day of the year is of the same length as 
the 14th of August? 

2. How many miles make a degree of longitude in the 
latitude of Lisbon? 

3. At what hour is the sun due east at London on the 
5th of May ? 

4. There is a place in the parallel of 31 deg. of north 
latitude, which is 31 deg. distant from London ; what 
place is it ? 

5. If the sun’s meridian altitude at London be 30 
deg. what day of the month, and what month is it ? 

6. On what month and day is the sun’s meridian alti¬ 
tude at Paris equal to the latitude of Paris ? 

7. When y Draconis is vertical to the inhabitants of 
London at ten o’clock at night, what day of the month, 
and what month is it ? 

8. What is the equation of time dependent on the 
obliquity of the ecliptic on the 14th of July ? 


309 


A PROMISCUOUS COLLECTION 


9. I observed the pointers in the Great Bear, on the 
meridian of London, at eleven o’clock at night ; in what 
month and on what night did this happen ? 

10. On what day of the inouth, and in what month, 
livill the shadow of a cane, placed perpendicular lo (he 
horizon of London, at ten o’clock in the morning, be ex¬ 
actly equal in lengtli to the cane ? 

11. The earth goes round the sun in 365 days 6 hours 
nearly ; how many degrees does it move in one day, at 
a medium ? Or, what is the daily apparent mean mo^ 
tion of the sun ? 

12. The moon goes once round her orbit, from the 
first point of the sign Aries to the same again, in 27 
days 7 hours 43 minutes 5 seconds ; what is her mean 
motion in one day ? 

13. The moon turns round her axis from the sun to 
the sun again, in 29 days 12 hours 44 minutes 3 sec¬ 
onds, which is exactly the time that she takes to go 
round her orbit from new moon to new moon ; at what 
rate per hour are the inhabitants (if any) of her equatori¬ 
al parts carried per hour by this rotation ? The moon’s 
diameter being 2144 miles. 

14. How many degrees does the motion of the moon 
exceed the apparent motion of the sun in 24 hours ? 

15. The day of the month being given, it is required 
to find the moon’s longitude when she is eight days old. 

16. Travelling in an unknown latitude I found, by- 
chance, an old horizontal dial ; the hour lines of which 
were so defaced by time that I could only discover 
those of IV and V, and found their distance to be ex¬ 
actly 21 degrees; for what latitude was the dial 
made ? 

17. Required the duration of twilight at the south 
pole. 

18. How far must an inhabitant of London travel 
southward to lose sight of Aidebaran ? 

19. What is the elevation of the north polar star a- 
bove the horizon of Calcutta? 

20- Lord Nelson beat the Frefich fleet near latitude 
31 deg. 11 min. north, longitude 30 deg. 22 min. east; 
point oiP the place on the globe. 

21. Wha* !- (be sun’s altitude at three o’clock in the 
afternoon at Philadelphia on flie 7 th of May ? 


OF EXERCISES ON THE GLOBES. 


310 


2*2. What is the lengtii of the day at London on the 
26ihof July, and how many degrees must the sun’s de¬ 
clination be diminished to make the day an hour shorU 
er ? 

23. At what hour does the sun first make his appear¬ 
ance at Peler^burg on the 4th of June ? 

24. At what rate per hour are (he inhabitants of Bot¬ 
any Bay carried from west to east by the rotation of the 
earth on its axis ? 

25. When Arclurus is 30 deg. above the horizon of 
London, and eastward of the meridian, on the 5th of No¬ 
vember, what o’clock is it ? 

26. Describe an horizontal dial for the latitude of 
W'^ashington. 

27. Describe a vertical dial facing the south, for the 
latitude of Edinburgh. 

28. What is the moon’s greatest altitude to the inhabi¬ 
tants of Dublin? 

29. What is (he sun’s greatest meridian altitude at 
the southern extremity of Patagonia ? 

30. At what hour at London, on the 15th of August, 
will the Pleiades be on the meridian of Philadel¬ 
phia ? 

31. If a comet, whose longitude was 4 signs 5 deg. 
and latitude 44 deg. north, appeared in Ursa Major, in 
what part of the constellation was it ? 

32. On what point of the compass does the sun set at 
Madrid when constant twilight begins at London ? 

33. What is the difference between the duration of 
twilight at Petersburg and Calcutta, on the first of Feb¬ 
ruary ? 

34. How much longer is the tenth of December at 
Madras than at Archangel ? 

35. How much longer is the 5th of May at Archan¬ 
gel than at Madras ? 

36. When it is two o’clock in the afternoon at Lon¬ 
don, on the 15th of February, to what place is the sun 
rising and setting, and where is it noon ? 

37. Does the sun shine over the north or south pole 
on the 17th of April, and how far ^ 

38. At what hour on the 18fh of April will the sun’s 
altitude and azimuth, from the east towards the south, 
be 40 deg. at London ? 


311 


A PROMISCUOUS COLLECTION 


39. Which way must a ship steer from Rio Janeiro to 
the Cape of Good Hope ? 

40. Are the clocks at Philadelphia faster or slower 
than those at London, and how much ? 

41. Are the clocks at Calcutta faster or slower than 
the clocks at London, and how much ? 

42. What is the difference of Latitude between Co¬ 
penhagen and Venice ? 

43. There is a place in latitude 31 deg. 11 min. north, 
situated, by an angle of position, south-east dy east A 
east from London ; what place is that, and how far is it 
from London in English miles ? 

44. On the 13th of February, 1813, the longitude of 
Venus was 9 signs 29 deg. 2 min. latitude 0 deg, 14 
min. south ; did Venus rise before or after the sun, and 
how much T 

45. On the 7th of December, 1813, the longitude of 
Venus wars 10 signs 0 deg. 51 min. latitude 2 deg. 26 
inin. south ; did Venus rise before or after the sun, and 
how much ? 

46. On the 19th of October, 1813, the longitude of 
the planet Jupiter was 5 signs 3 deg. 41 min. latitude 0 
deg. 52 min. north ; at what hour did he rise, come to 
the meridian, and set at London ? 

47. On the 7th of January, 1813, the moon’s longi¬ 
tude at midnight was 11 signs 22 deg. 20 min. latitude 2 
deg. 47 min. south; required her rising amplitude at 
London, and the hour and azimuth, when she was 30 deg. 
above the horizon. 

48. The moon’s longitude on the 5(b of November, 
1813, at midnight, was 0 signs 9 deg. 21 min. latitude 
4 deg. 31 min. south ; required the time of her rising, 
coming to the meridian, and setting at London, and the 
time of high water at London Bridge. 

49. To what places of the earth was the moon 
vertical, on the first of January, 1813, her longitude be¬ 
ing 9 signs 2 deg. 49 min. and latitude 3 deg. 48 min. 
north ? 

50. On the 1st of March, 1813, the moon’s ascending 
node was 4 signs 18 deg. 39 min.; where will the de¬ 
scending node be ? 

51. The moon’s declination on the lOtli of November, 
1813, was 20 deg. 8 min. north ; to what places of the 
earth was she vertical ? 


OF EXERCISES ON THE GLOBES. 312 

5*2. What stars are constantly above the horizon of 
Copenhagen ? 

53. 1 observed the altitude of Betelguese to be 19 
deg. and that of Aldebaran 40 deg.; they both appear¬ 
ed in the same azimuth, viz. exactly east ; what lati¬ 
tude was I in ? 

54. In what latitude is Aldebaran on the meridian 
when j8 in the Lion’s Tail is rising ? 

55. In what latitude is Rigel setting when Regulus is 
on the meridian ? 

56. In what latitude are the pointers in the Great 
Bear on the meridian when Vega is rising ? 

57. In latitude 79 deg. north, on the 1st of February, 
at what hour will Procyon and Regulus have the same 
altitude ? 

58. At what hour on the 10th of February, will Ca- 
pella and Procyon have the same azimuth at London ? 

59. On the 10th of November, at eight o’clock in the 
evening, Bellatrix in the left shoulder of Orion was ris¬ 
ing ; what was the latitude of the place T 

60. On the 16th of February, Arcturus rose at eight 
o’clock in the evening ; what was the latitude ? 

61. At what hour of the night, on the 16th of Febru¬ 
ary, will the altitude of Regulus be 28 deg. at London ? 

62. Required the altitude and azimuth of Markab in 
Pegasus, at London, on the 21st of September, at nine 
o’clock in the evening. 

63. On what day of the month, and in what month, 
will the pointers of the Great Bear be on the meridian of 
London at midnight ? 

64. W'hat inhabitants of the earth have the greatest 
portion of moon-light ? 

65. On what day of the year will Altair, in the Ea¬ 
gle, come to the meridian of London with the sun ? 

66. In what latitude north is the length of the longest 
day eleven times that of the shortest ? 

67. In what latitude south is the longest day eighteen 
hours ? 

68. At what time does the morning twilight begin, 
and at what time does the evening twilight end at Phila¬ 
delphia, on the 15th of January ? 

69. When it is four o’clock in the afternoon at^ Lon¬ 
don, on the 4th of J une, where is it twilight ? 

42 


313 


A PROMISCUOUS COLLECTION 


70. Required the antipodes of Cape Horn. 

71. Required the periceci of Philadelphia. 

72. Required the antceci of the Sandwich Islands. 

73. What is the angle of position between London and 
Jerusalem ? 

74. Required the distancebetween London and Alex¬ 
andria, in English and geographical miles. 

75. In what latitude north does the sun begin to shine 
constantly on the lOtli of April ? 

76. How long does the sun shine without setting at 
the north pole, and what is the duration of dark night ? 

77. Where is the sun vertical when it is midnight at 
Dublin on the 15th of July ? 

78. When it is five o’clock in the evening at Phila¬ 
delphia, where is it midnight, and where is it noon ? 

79. What places have the same hours of the day as 
Edinburgh ? 

80. What places have opposite hours to the respec¬ 
tive capitals of Europe ? 

81. At what hours at London, is the sun due east at 
the time of the equinoxes ? 

82. At what hour at London, is the sun due east at 
the time of the solstices? 

83. In what climates are the following places situated, 
viz. Philadelphia, Madrid, Drontheim, Trincomale, Cal¬ 
cutta, and Astracan ? 

84. On what day of the year does Regulus rise heli- 
acally at London ? 

85 .On what day of the year does Betelguese set heli- 
acally at London ? 

86. What stars set acronycally at London on the 24th 
of December ? 

87. What stars rise acronycally at London on the 
12th of December ? 

88. In what latitude north do the bright stars in the 
head of the Dolphin, and Altair in the Eagle, rise at the 
same hour ? 

89. In what latitude north do Capella and Castor set 
at the same hour, and what is the difference of time be¬ 
tween their coming to the meridian ? 

90. What stars rise cosmically at London on the 7th 
of December ? 


OF EXERCISES ON THE GLOBES. 


QU 


91. What stars set cosmicalfy at London on the 10th 
of December ? 

92. What degrees of (he ecliptic and equinoctial rise 
with A-ldebaran at London? 

93. On what day of the year does Arclurus come to 
the meridian of London, at two o’clock in the morning ? 

94. On what day of the year does Regulus come to 
the meridian of London, at nine o’clock in the evening ? 

95. At what time does Vega in Lyra come to the 
meridian of London, on the 18th of August ? 

96. Trace out the Galaxy or Milky-way on the celes- 
tial globe. 

97. If the meridian altitude of the sun on the 7th of 
June be 50 deg. what is the latitude of the place ? 

98. Required the sun’s right and oblique ascension 
at London, at the equinoxes. 

99. Required the sun’s right ascension, oblique as¬ 
cension, ascensional difference, and time of rising and 
setting at London, on the 5th of May. 

100. If the sun’s rising amplitude on the 7th of June 
be 24 deg. to the northward of the east, what is the latL 
tude of the place ? 

101. What stars have the following degrees of right 
ascensions and declinations ? 


162° 49'R.A 62° 50' D.N. 
244 17 R.A.25 58 D S. 
238 27 R.A.19 15 D.S. 
suu'dial for the latitude 


7° 10' R.A.29°45' D.N. 

14 38 R.A.34 33 D.N. 

135 59 R.A. 3 10 D.N. 

102. Describe a horizontal 
of Edinburgh. 

103. What is the length of the day on the 14th of Feb¬ 
ruary at London, how much must the sun’s declination 
increase to make the day an hour longer ? 

104. What hour is it at London when it is 17 minutes 
past 4 in the evening at Jerusalem ? 

105. On the 21st of June, the sun’s altitude was ob¬ 
served to be 46 deg. 25 rain, and his azimuth 112 deg. 
59 min. from the north towards the east, at London ; 
what was the hour of the day ? 

106. Given the sun’s declination 17 deg. 6 min. north, 
and increasing ; to find the sun’s longitude, right ascen¬ 
sion, and the angle formed between the ecliptic and the 
ineridian passing through the sun* 




315 


A PROMISCUOUS COLLECTION 


tor. Given the sun’s right ascension 134 deg. 54 rain, 
to find his longitude, declinati«)n, and ihe angle formed 
between the ecliptic and the meridian passing through 
the sun. 

108. Given the sun’s longitude 17 deg. 34 min. in 8 ; 
to find his declination, right ascension, and the angle 
formed between the ecliptic and the meridian passing 
through the sun. 

lOd. Given the sun’s amplitude 39 deg. 50 rain, from 
the east towards the north, and his declination *23^ deg. 
north ; to find the latitude of the place, the time of the 
sun’s rising and setting, and the length of the day and 
night. 

110. At what time on the first of April, will Arcturus 
appear upon the 6 o’clock hour-line at London, and what 
will his altitude and azimuth be at that time ? 

111. Required the altitude of the sun, and the hour 
he will appear due east at London, on the 20th of May. 

112. At what hours will Arcturus appear due east and 
west at London, on the 2d of April, and what will its al¬ 
titude be ? 

113. At London, the sun’s altitude was observed to 
be 25 deg. 30 min. when on the prime vertical; required 
his declination and the hour of the day. 

114. On the 2d of April, 1813, the moon’s right as¬ 
cension at midnight was 35 deg. 44 min. and her de¬ 
clination 8 deg. 57 min. north ; required her distance 
from Regulus, Procyon, and Betelguese, at that time. 

115. The distance of a comet from Sirius was observ¬ 
ed to be 66 deg. and from Procyon 51 deg. 6 min. ; the 
comet was westward of Sirius ; required its latitude and 
longitude. 

116. On the 29th of January, in latitude 53 deg. 24 
min. north, and longitude 25 deg. 18 min. west, at 14 
hours 58 min. by a watch well regulated; the altitude 
of Procyon was 19 deg. 54 min. and that of Alphacca 
was 42 deg. 9 min. as observed by two separate per¬ 
sons ; Alphacca was on the east, and Procyon on the 
west of the meridian ; was the watch too fast or too 
slow ? 

117. The declination of yin the head of Draco is 51 
deg. 31 rain, north ; to what places will it be vertical 
when it comes to their respective meridians ? 


OF EXERCISES ON THE GLOBES. 


316 


118. When it is four o’clock in the evening at Lon¬ 
don on the 4th of May, to what places is the sun rising 
and setting, where is it noon at midnight, and to what 
place is the sun vertical ? 

119. At what time does the sun rise and set at the 
North Cape, on the north of Lapland, on the 5th of 
April, aiui ‘Ahat is the length of the day and night ? 

120. At what lime does the sun rise at the Shetland 
Islands, when it sets at four o’clock in the afternoon at 
Cape Horn ? 

121. Walking in the Kensington Gardens on (he 17th of 
May, it was twelve o’clock by the sun*dial, and wanted 
eitht minutes to twelve by my watch ; was my watch 
right ? 

122. If the sun set at nine o’clock, at what time 
do s it rise, and what is the length of the day and 
ni;,-ht ? 

123 Where is the sun vertical when it is five o’clock 
in the morning at London, on the 15th of May T 

124. At what hour does day break at London on the 
5th of April ? 

125. if the moon be five days old on the first of June, 
at what time does she rise, culminate, and set at Lon¬ 
don ? 

126. On what day of the month, and in w hat month, 
does the sun rise 24 deg. to the north of the east, at 
London ? 

127. When the sun is rising to the inhabitants of Lon¬ 
don on the 8lh of May, where is it setting ? 

128. When the sun is setting to the inhabitants of 
Calcutta on the 18th of March, where is it midnight T 

129. What is the difference between the circumfer¬ 
ence of the earth at the equator and at Petersburg, in 
English miles ? 

130. At what hour does the sun rise at Barbadoes 
when constant twilight begins at Dublin ? 

131. When the sun is rising at O’why’hee, on the 
18*h of May, where is it noon ? 

132. At what hour does the sun rise at London when 
it sets at seven o’clock at Petersburg ? 

133. How high is the the north polar star above the 
horizon of Quebec ? 


317 


A PROMISCUOUS COLLECTION 


134. How many English miles must an inhabitant of 
London travel southward, that the meridian altitude of 
the north polar star be diminished *25 deg. ? 

135. How many English miles must I travel 
westward from Loudon, that my watch may be seven 
hours too fast ? 

136. What place of (he earth has the sun in the zenith 
when it is seven o’clock in the morning at London, on 
the 25th of April ? 

137. On what day of the month, and in what month, 
is the sun’s amplitude at London equal to one-third of 
the latitude ? 

138. On what month, and day is the sun’s amplitude 
at London equal to the latitude of Kingston in Jamai¬ 
ca ? 

139. If the moon be three days old on the 17th of 
February, what is her longitude ? 

140. If (he highest point of Mont Blanc be 5101 
yards above the level of the sea, what would be its alti¬ 
tude on a globe of 18 inches in diameter ? 

141. If the polar diameter of the earth be to the equa¬ 
torial diameter as 229 is to 230, what would the polar 
diameter of a three inch globe be, if constructed on (his 
principle ? 

142. What inhabitants of the earth, in the course of 
12 hours, will be in the same situation as their anti- 

On what day of the year at London, is the twi¬ 
light eight hours long ? 

144. At what time does the sun rise and set at Lon¬ 
don, when the Inhabitants of the north pole begin to 
have dark night ? 

145. At what hour does the sun set at the Cape of 
Good Hope, when total darkness ends at the north pole ? 

146. What is the moon’s longitude when full moon 
happens on the 5th of April ? 

147. Does the sun ever rise and set at the north 
pole ? 

148. At what hour of the day, on the 15th of April, 
will a person at London, have his shadow the shortest 
possible ? 

149. If the precession of the equinoxes be 50^ secr 


podes r 
143. 


OP EXERCISES ON THE GLOBES. 3101 

onda in a year, how many years will elapse before the 
constellation Aries will coincide with the solsticial co¬ 
lure ? 

150. If the obliquity of the ecliptic be continually di¬ 
minishing, at the rate of 56 seconds in a century, as sta¬ 
ted by several authors, how many years willelapse from 
the first of January, 1805, when the obliquity of the e- 
cliptic was 23 deg. 27 min. 52. 8 sec. before the ecliptic- 
will coincide with the equator? 

151. Required the duration of dark night at the south 
of Nova Zeiubla. 

152. When constant twilight ends at Petersburg,* 
where is the day 18 hours long ? 

153. At what hour does the sun set at Constantinople 
when it rises 12 deg. to the north of the east ? 

154. What is the difference between a solar and a si- 
derial year, and what does the difference arise from ? 

155. What is the difference between the length of a 
natural or astronomical day and a siderial day, and how 
does the difference arise ? 

156. Required the difference between the length of 
the longest day at Cape Horn and at Edinburgh. 

157. If one man were to travel eight miles a day west¬ 
ward round the earth at the equator, and another two 
miles a day westward round it in the latitude of 80 deg. 
north ; in how many days would each of them return to 
the place whence he set out ? 

158. If a pole of 18 feet in length be placed perpen¬ 
dicular to the horizon of London, on the 15th of July, 
and another exactly of the same length be placed in a 
similar manner at Edinburgh, which will cast the longer 
shadow at noon ? 

159. If the moon be in 29 deg. of Leo at the time of 
new moon, what sign and degree will she be in when she 
is five days old ? 

160. What is the duration of constant day or twilight 
at the north of Spitzbergen ? 

161. What place upon the globe has the greatest lon¬ 
gitude, the least longitude, no longitude, and every lon¬ 
gitude ? 

162. In what latitude is the length of the longest day, 
to the length of the shortest, in the ratio of 3 to 2 ? 


319 aUESTIONS FOR THE EXAMINATION 

163. If a man of 6 feet high were to travel round the 
earth, how much farther would his head go than his 
feet ? 


CHAP. II. 


A Collection of Questions^ with References to the Pages 
where the Ansrvers will be found ; designed as an As¬ 
sistant to the Tutor^ in the Examination of the Shi- 
dent* 


I. Great circles on the terrestrial globe* 

1. WHAT is a Great Circle, and how many are there 
drawn on the terrestrial globe ? Definition 6, page 3. 

2. What is the equator, and what is its use ? Def* 9, 
page 3. 

3. What are the meridians, and how many are drawn 
on the terrestrial globe ? Def* 8, page 3. 

4. What is the first meridian ? Def* 10 , page 3. 

5* What is the ecliptic, and where is it situated ? 
Def. 11 , page 3. 

6. What are the colures, and into how many parts do 
they divide the ecliptic ? Def 42, page 10. 

7* What are the hour-circles, and how are they drawn 
on the globe ? Def .50, page 11. 

8. What hour-circle is called the 6 o’clock hour line 7 
Def* 51, page 11. 

9. What are the azimuth or vertical circles, ^nd what 
is their use ? Def 43, page 10. 

10. What is the prime vertical? Def 44, page 10. 


* Though a reference be given to the pages where the answers to 
each question may be found ; yet, perhaps it would be better for the 
student not to learn the answers by heart, verbatim from the book ; but 
to frame an answer himself, from an attentive perusal of his lesson ; by 
which means, the understanding will be called into exercise as well as 
the memory. ^ 



OP THE STUDENT. 


320 


II. Small circles on the terrestrial globe, 

1. What is a small circle, and how many are generally 
drawn on the terrestrial globe ? Def. 7, page 3. 

2. What are the tropics, and how far do they extend 
from the equator, &c. ? Def. 15, page 5. 

3. What are the polar circles, and where are they 
situated? Def. 16, page 5. 

4. What are the parallels of latitude, and how many 
are generally drawn on the terrestrial globe ? Def. it, 
page 5. 

5. vV^hat circles are called Almacanters ? Def, 39, 
page 9. 

III. Great circles on the celestial globe, 

1. How many great circles are drawn on the celes¬ 
tial globe ? 

2. The lines of terrestrial longitude are perpendicular 
to the equator, on the terrestrial globe, and all meet in 
the poles of the world ; to which great circle on the 
globe are the lines of celestial longitude perpendicular, 
and on what points of the globe do they all meet ? 

3. What are the colures, and into how many parts do 
they divide the ecliptic ? Def. 42, page 10. 

4. What is the equinoctial, and what is its use? Defo 

9, page 3. < 

5. What is the ecliptic, and where is it situated ? Def, 
11, page 3. 

6. What is the zodiac, and into how many parts is it 
divided I Def. 12, page 4. 

7. What are the signs of the zodiac, and how are they 
marked ? Def. 13, page 4. 

8. Which are the spring, summer, autumnal, and 
winter signs ; and on what days does the sun enter them? 
Def. 13, page 4. 

9. Which are the ascending and descending signs . 
Def. 13, page 4. 

IV. Small circles on the celestial globe, 

I. How many small circles are drawn on the celestial 
globe ? 


43 


321 QUESTIONS FOR THE EXAMINATION 

2. What are the tropics, and how far do they extend 
from the equinoctial ? Def. 15, page 5. 

3. What are the polar circles, and where are they 
situated ? Def, 16, page 5. 

4. What are the parallels of celestial latitude ? Def* 
40, page 10. 

5. What are the parallels of declination ? Def 41, 
page 10. 

V. The brass meridian, and other appendages to the 
globes. 

1. What is the brazen meridian, and how is it divided 
and numbered ? Def. 5, page 2. 

2. What is the axis of the earth, and how is it repre¬ 
sented by the artificial globes ? Def. 4, page 2. 

3. What are the poles of the world ? Def. 4, page 2. 
4 What are the hour circles, and how are they divi¬ 
ded ? Def. 18, page 5. 

5. What is the horizon, and what is the distinction 
between the rational and sensible horizon ? Def. 19,20, 
and 21, page 6. 

6. W hat is the wooden horizon, and how is it divided ? 
Def 22, page 6. 

7. What is the mariner’s compass, how is it divided I 
and what is the use of it on the globe ? Def 32, 33, and 
note, page' 8. 

8. What is the quadrant of altitude, how is it divided, 
and what is its use ? Def. 36, page 9. 

VI. Points on, and belonging to the globes. 

1. What is the pole of a circle ? Def 28, page 7. 

2. What is the zenith, and of what circle is it the 
pole ? Def 26, page 7. 

3. What is the nadir, and of what circle is it the pole, 
Def 27, page 7. 

4 What are the cardinal points of the horizon ? Def 

23, page 7. 

5. What are the cardinal points in the heavens? Def. 

24, page 7. 

6. What are the cardinal points of the ecliptic ? Def 

25, page 7. 


OF THE STUDENT. 


322^ 


7. What are the equinoctial points ? Def, 29, page 7. 

8. What are the solstitial pomis ? De/. 80, page 8. 

9. What is the culminating point ol a star, or of a 

planet? 52, page 12. 

10. What are the poles of the ecliptic, how far are 
they from the poles of the world, and in what circles are 
they situated ? 

VII Latitude and longitude of the terestrial globe, the 

division of the globe into sones and climates, the 

position oj the sphere, the shadows, and positions of 

the inhabitants with respect to each other, &c» 

1. What is the latitude of a place on the terrestrial 
globe ? Def 34, page 9. 

2. What is the longitude of a place on the terrestrial 
globe ? Def. 37, page 9. 

3. What is a zone, and how many are there on the 
terrestrial globe ? He/. 70, p.ige 18. 

4. What is the situation, and what is the extent of the 
torrid zone T Def 71, page 18. 

5. Where are the two temperate zones situated, and 
what is the extent of each ? Def 72, page 18. 

6. Where are the two frigid zones situated, and what 
is the extent of each ? Def 73, page 18. 

7 What is a climate, and how many are there on the 
globe? Def 69, page 15. 

8. Have all places in the same climate the same 
atmospherical temperature ? Note, page 15. 

9. How many different positions of the sphere are 
there ? Def 65, page 15. 

10. What is a right sphere, and what inhabitants of 
the globe have this position ? Def 66, page 15 ; see 
likewise Prob. XXII, page 192. 

11. What is a parallel sphere, and what inhabitants 
of the globe have this position ? Def 67, page 15; and 
Prob. XXII. page 192, &c. 

12. What is an oblique sphere, and what inhabitants 
of the globe have this position ? Def 68,page 15; and 
Prob. XXII, page 192, &c. 

13. What parts of the globe do the Amphiscii inhabit, 
and why are they so called ? Def 74, page 18. 


323 aUESTIONS FOB THE LAMINATION 

14. When do <he Amphiscii obtain the name of As¬ 
cii ? 

15. What parts of the globe do the Heteroscii inhabit, 
and why are they so called ? Def* 7by page 18. 

16. What parts of the globe do the Periscii inhabit, 
and why are they so called ? Def. 76, page 19. 

17. What inhabiiants are called Antceci to each other, 
and what do you observe with respect to their latitudes, 
longitudes, hours, &c. ? Def. 77y page 19 

18. What inhabitants are called Periceci to each 
other, and what is observed with respect to their lati¬ 
tudes, longitudes, hours, seasons, &c. ? 

19. What are the Antipodes, and what is observed 
with respect to their seasons of the year, &c. ? Def. 79, 
page 19. 

VIII. Latitudes and longitudes of the stars and plan¬ 
ets on the celestial globcy &c. together with the poeti¬ 
cal rising and setting of the starSy &c. 

1. What is the latitude of a star or planet ? Def 35, 
page 9. 

2. What is the longitude of a star or planet ? Def. 
38, page 9. 

3. What are the fixed stars, and why are they so cal¬ 
led ? Def 88, page 22. 

4. What is a constellation, and how many are there 
on the celestial globe ? Def 90, page 22 ; see the tables, 
pages 23, 24, 25, 26, and 27. 

5. What is meant by the poetical rising and setting of 
the stars ? Def 89, page 22. 

6. When is a star said to rise and set cosmically ? 

7. When is a star said to rise and set acronycally ? 

8. When is a star said to rise and set heliacally ? 

9 .What is the Via Lactea, and through what constel* 
lations does it pass ? Def 91, page 34. 

10. What kind of stars are termed Nebulous ? Def. 
92, page 34. 

11. How are the stars, which have not particular 
names, distinguished on the celestial globe ? Def, 93, 
page 34. 


324 


OF THE STUDENT. * 

IX, Definitions and terms common to both the globes, 

1. What is the declination of the sun, a star, or plan- 
et ? Def. 14, page 4. 

2. What is a hemisphere ? Def. 31, page 8. 

3. What is the altitude of any object in the heavens ? 
Def. 45, page 10. 

4. What is the meridian altitude of the sun, a star, or 
planet ? 

5. What is the zenith distance of a celestial object ? 
Def. 46, page 10. 

6. What is the polar distance of a celestial object ? 
47, page 11. 

7. What is the amplitude of a celestial object ? Def. 

48, page 11. 

8. What is the azimuth of a celestial object ? Def, 

49, page 11. 

9. What is the right ascension of the sun, or of a star. 
Sec. ? Def. 80, page 19. 

10. What is the oblique ascension of the sun, or of a 
star, &c. ? Def. 81, page 19. 

11. What is the oblique descension of the sun, or of 
a star. Sec. ? Def 22, page 19. 

12. What is the ascensional or descensional differ¬ 
ence ? Def. 83, page 19. 

X. Time—Yearsy Days, &c. 

1. What is a solar or tropical year, and what is the 
length of it ? Def. 62, page 14. 

2. What is a siderial year, and what is its duration ? 
Def. 63, page 14. 

3. What is an astronomical day ? Def 58, page 13. 

4. What is a mean solar day ? Def. 57, page 12. 

5. What is a true solar day ? Def 56, page 12. 

6. What is an artificial day ? Def. 59, page 13. 

7. What is a civil day ? Def. 60, page 13. 

8. What is a siderial day ? Def 61, page 13. 

9. What is meant by apparent noon, or apparent 
time ? Def. 53, page 12. 

10. What is true or mean noon ? Def. 54, page 12. 

11. What is the equation of time at noon ? Def. 55, 
page 12. 


325 aUESTIONS FOR THE EXIMINATION 

XI. Astronomical and Miscellaneous Definitions^ &c» 

1. What do you understand by the precession of the 
equinoxes, and in what time do they make an entire rev¬ 
olution round the equinoctial ? Def. 64, page 14. 

2. What is the crepusculum or twilight, and what is 
the cause of it ? Def. 84, page 20. 

.3. What is refraction, and whence does it arise T 
Def. 85, page 20. 

4. What is an angle of position, and in what does it 
differ from a bearing by the mariner’s compass ? Def, 
86, page 21, and note page 178. 

5. AVhdt are rhumbs and rhumb-lines ? Def. 87, 
page 21. 

6. What are the planets, and how many belong to the 
solar system ? Def. 94 and 95, pages 35 and 36. 

7. What is the distinction between primary and sec¬ 
ondary planets, and how many secondary planets belong 
to the solar system ? Def. 96, page 36. 

8. What is the orbit of a planet ? Def. 97, page .36. 
Of what figure are the orbits of the planets, and in what 
part of the figure is the sun placed ? page 129. 

9. What are the nodes of a planet ? Def 98, page 36. 

10. What are the different aspects of the planets, and 
how many are there ? Def. 99, page 36. 

11. What are the syzygies and quadratures of the 
moon ? 

12. When is a planet’s motion said to be direct, sta¬ 
tionary, or retrograde ? Def. 100, 101, and 102, page 
37. 

13. What is a digit ? Def. 103, page 37. 

14. What is the disc of the sun or moon ? Def 104, 
page 37. 

15. What are the geocentric and heliocentric latitudes 
and longitudes of the planets 1 Def. 105, and 106, page 
37. 

16. When is a planet said to be in apogee ? Def. 107, 
page 37. 

17. When is a planet said to be in perigee ? Def. 
108, page 37. 

18. What is the aphelion or higher apsis of a planet’s 
orbit ? Def. 109, page 37. 

19. What is the perihelion or lower apsis of a planet’s 
orbit? Def. 110, page 37. 


OF THE STUDENT. 326 

20. What is the line of the apsides ? Def. Ill, page 

sr. 

21. What is the eccentricity of the orbit of a planet ? 
J)eJ\ 112, page 37. 

22. What is the elongation of a planet T Def, 117, 
pa^e 38. 

23. What are the occultation and transit of a planet ? 
Def 113 and 114, page 37. 

24. What is the cause of an eclipse of the sun I Def 
115, page 38. 

2>. What is the cause of an eclipse of the moon ? 
Def 116, page 38. 

26. What are the nocturnal and diurnal arcs descri¬ 
bed by the heavenly bodies? Def 118 and 119, page 
38. 

27. What is the aberration of a star ? Def 120, page 
38. 

28. What are the centripetal and centrifugal forces ? 
Def 121 and 122, page 38. 

29. What is gravity ? Def 8, page 44. 

30. What is the vis inertiae of a body ? Def 9, page 44. 

31. What are the general properties of matter? Def 
1 and 2, page 42. 

32. Can matter be divided ad infinitum ? pages 43 
and 44. 

33. What is motion, and what is the distinction be¬ 
tween absolute and relative motion ? Def 6, page 43,, 
and Def 10, page 44. 

34. What are Sir Isaac Newton’s three laws of mo¬ 
tion ? pages 45 and 46. 

35. What is compound motion ? page 46. 

XII. Of the solar system and the sun. 

1 . What is the solar system,and why is it so called? 
page 124. 

2. What part of the solar system is called the centre 
of the world? page 124. 

3. D<)es not the sun revolve on its axis, and what oth¬ 
er motion has it? pages 124 and 125. 

4. Of what shape is the sun, how far is it from the 
earth, and how many miles is it in diameter ? 

5. What is the comparative magnitude between the 
,sun and the earth ? page 126.. 


327 aUESTIONS FOR THE EXAMINATION 
XIII. Of Mercury, 

1. What is the length of Mercury’s year? page 127'. 

2. What is the greatest elongation of Mercury ? page 
127. 

3. What is the distance of Mercury from the sun ? 

4. What is the diameter of Mercury ? page 127. 

5. What is the comparative magnitude between 
Mercury and the earth ? 

6. What is the comparison between the light and heat 
which Mercury receives from the sun, and the light and 
heat which the earth receives ? 

7. At what rate per hour are the inhabitants of Mer*- 
cury (if any) carried round the sun ? page 128. 

XIV. Of Venus, 

1. When is Venus an evening star, and in what situa¬ 
tion is she a morning star ? page 129. 

2. How long is Venus a morning star ? page 129. 

3. In how many days does Venus revolve round the 
sun ? 

4. The last transit of Venus over the sun’s disc hap¬ 
pened in 1769, when will the next transit happen ? 

5. What is the opinion of Dr. Herschel respecting 
the mountains in Venus ? 

6. What is the opinion of M. Schroeter on the same 
subject ? page 138 in the notes. 

7. What is the greatest elongation of Venus ? page 
130. 

8. W^hat is the diameter of Venus ? page 130. 

9. What is the magnitude of Venus ? 

10. What is the distance of Venus from the sun ? 

11. What is the comparison between the light and 
heat which Venus receives from the sun, and the light 
and heat which the earth receives ? 

12. At what rate per hour does Venus move round 
the sun ? 


XV. Of the Earth, 

1. What is the figure of the earth ? page 52. 

2. Why is the earth represented by a globe ? pages 
57 and 58, 


OF THE STUDENT. 33S 

3. What proofs hare we that the earth is globular ? 
pages 52 and 53. 

4. What would be the elevation of Chimborazo, the 
highest of the Andes mountains, on an artificial globe of 
18 inches diameter ? page 54, the note. 

5. What is a spheroid, and how is it generated ? page 
44, the note. 

6. What is the difference between the polar and equa. 
torial diameters of the earth ? page 55, and the note. 

7. What is the length of a degree ? page 57, and the 
note. 

8. What is the use of finding the length of a degree, 
and how can the magnitude of the earth be determined 
thereby? page 57. 

9. Who was the first person who measured the length 
of a degree tolerably accurate ? page 57. 

10. What is the length of a degree according to the 
French admeasurement ? page 57, the note. 

11. In what time does the earth revolve on its axis 
from west to east ? page 58, and Def. 61, page 13 and 
the note. 

12. What is the diameter of the earth; what is its cir¬ 
cumference, and how are they determined ? page 57, 
and the note. 

13. What proofs can you give of the diurnal motion of 
the earth ? pages 59 and 60. 

14. How do you explain the phenomena of the appa¬ 
rent diurnal motion of the sun ? pages 60 and 61. 

15. What proofs can you give of the annual motion of 
the earth ? page 61. 

16. What is the distance of the earth from the sun^ 
and how is it calculated? page 62, and the note. 

17. At what rate per hour does the earth travel round 
the sun ? page 63. 

18. At what rate per hour are the inhabitants of the 
equator carried from west to east by the revolution of the 
earth on its axis, and at what rate per hour are the in¬ 
habitants of London carried the same way ? page 63. 

19. How do you explain the motion of the earth 
round the sun ? page 64. 

20. How do you illustrate the phenomena of the dif¬ 
ferent seasons of the year ? pages 63, 64, and 65. 

44 


339 GtUESTIONS FOR THE EXAMINATION 
XVI. Of the Moon. 

1. How many kinds of lunar months are there ? page 
132. 

2. What is a periodical month ? 

3. What is a synodical month ? 

4. When is the eccentricity of the moon’s elliptical 
oi'bit the greatest ? 

5. When is the eccentricity of the moon’s elliptical 
orbit the least? page 132. 

6. Does the motion of the moon’s nodes follow, or re¬ 
cede from the order of the signs ? 

7. In how many years do the moon’s nodes form a 
complete revolution round the ecliptic ? 

8. In what space of time does the moon turn on her 
axis ? page 133. 

9. What is the libration of the moon ? 

10. Is the path of the moon convex, or concave to¬ 
wards the sun ? page 133. 

11. Please to explain the different phases of the moon, 
pages 134, and 135. 

12. What point on the earth has a fortnight’s moon¬ 
light and a fortnight’s darkness, alternately I pages 135, 
and 195. 

13. What is the moon’s mean horizontal parallax, and 
at what distance is she from the earth ? page 136. 

14. What is the magnitude of the moon when com¬ 
pared with that of the earth ? 

15. How many miles is the moon in diameter ? 

16. In how many days does the moon perform her 
revolution round the earth, and at what rate does she 
travel per hour? page 136. 

17. In what manner have astronomers described the 
different spots on the moon’s surface ? 

18. Have not astronomers discovered volcanoes, 
mountains, &c. in the moon ? pages 137 and 138. 


XVIL Of Mars. 

1. What is the general appearance of Mars ? page 
139. 


OP THE STUDENT. 340 

'2. In what time does Mars revolve on his axis ^ naffe 
140. ^ ^ 

3. In what time does Mars perform his revolution 
round the sun, and at what rate does he travel per hour? 
page 140. 

4. How far is Mars distant from the sun ? 

5. How many miles is Mars in diameter ? 

6. What is the comparative magnitude between Mars 
and the earth ? 

XVIII. Of Ceres, Pallas, Juno, and Vesta, 

1. When, and by whom, was the planet or Asteroid, 
Ceres discovered ? page 141. 

2. How many miles is Ceres in diameter ? 

3. What is the distance of Ceres from the sun, and 
what is the length of her year ? 

4. When and by whom was Pallas discovered ? 

5. What is the diameter of Pallas in English miles ? 

6. Who discovered the Planet Juno? 

7. By whom was Vesta discovered ? page 142. 

XIX. Of Jupiter, &c, 

1. In what situation is Jupiter a morning star, and in 
what situation is he an evening star? page 142. 

2. In what time does Jupiter revolve on his axis ? 

3. What are Jupiter’s belts ? 

4. In what time does Jupiter perform his revolution 
round the sun, and at what rate per hour does he travel ? 
page 143. 

5. What is the distance of Jupiter from the sun ? 

6. What is the diameter of Jupiter in English miles ? 

7. What is the comparative magnitude between Ju¬ 
piter and the earth ? 

8. What is the comparison between the light and heat 
which Jupiter receives from the sun, and the light and 
heat which the earth receives ? 

9. How many satellites is Jupiter attended by? page 
144. 

10. By whom were the satellites of Jupiter discover¬ 
ed ? 


341 aUESTIONS FOR THE EXAMINATION 

11. In what time do the respective satellites perform 
their revolutions round Jupiter ? 

12. In what manner are the longitudes of places de¬ 
termined by the satellites of Jupiter ? page 145. 

13. Please to explain the configuration of the satel¬ 
lites of Jupiter as given in the Xllth page of the Nauti¬ 
cal Almanac, pages 145 and 146. 

14. How was the progressive motion of light discov¬ 
ered ? page 147. 

XX.0/ SaiurUf &c, 

1. What is the appearance of Saturn when viewed 
through a telescope ? page 147. 

2. In what time does Saturn perform his revolution 
round the sun, and at what rate does he travel per hour ? 

3. What is the distance of Saturn from the sun ? 

4. How many English miles is Saturn in diameter, and 
what is his magnitude compared with that of the earth ? 
page 148. 

5. What is the comparison between the light and 
heat which Saturn receives from the sun, and the light 
and heat which the earth receives ? 

6. In what time does Saturn revolve on his axis ? 

7. How many moons is Saturn attended by, and by 
whom were they discovered f 

8. Is not the 7th satellite the nearest to Saturn, 
and, if so, why was it not called the first satellite ? page 
149. 

9. What is the ring of Saturn, and how may it be rep¬ 
resented by the globe ? pages 149, and 150. 

10. By whom was the ring of Saturn discovered ? 

11. In what time does the ring of Saturn revolve 
round the axis of Saturn ? 

XXI. Of the Georgian Planet, Sc» 

1. When and by whom was the Georgian planet dis¬ 
covered ? page 150. 

2. What is the appearance of the Georgian when view* 
ed through a tellescope ? page 151. 


OF THE STUDENT. 


342 


3. In what time does the Georgian planet revolve 
round the sun, and at what rate per hour does it travel ? 

4. What is the comparative magnitude between the 
Georgian planet and the earth f 

5. How many satellites belong to the Georgian ? 

6. By whom were the satellites of the Georgian dis¬ 
covered, and in what order do they perform their revo¬ 
lutions round the planet ? page 151. 

N. B. The tutor may extend these questions to Chap. F, FJ, FJJ, 
IX, and X. Part I. and to Chap, II, Part II; also to the manner of 
solving the different problemsy etc. 


343 


THE LATITUDES AND 


' CHAPTER III. 

A Table of the Latitudes and Longitudes of some of 
the Principal places in the Worlds with the Countries 
in which they are situated —iV. B. The Longitudes 
are reckoned from Greenwich Observatory, 


A. 


'Xames of Plaoes. 

Country or Sea. 

Latitudes. 

Q f 

Longitudes^ 

o f 

Abbeville 

France 

50 

7 

N. 

1 

49 

E. 

Aberdeen 

Scotland 

57 

9 

N. 

2 

28 

W. 

Abo 

Sweden 

60 

27 

N. 

22 

IS 

E. 

Acapulco 

Mexico 

17 

10 

N. 

101 

45 

W. 

Achen 

Sumatra I. 

5 

22 

N. 

95 

40 

E. 

Adrianople 

Turkey 

M 

10 

N. 

26 

SO 

E. 

Adventure Bay 

New Holland 

45 

23 

S. 

147 

SO 

E. 

Agra 

Hindoos tan 

26 

43 

N. 

76 

44 

E. 

Air 

•Scotland 

54 

25 

N. 

4 

26 


Aix 

France 

43 

32 

N. 

5 

26 

E. 

Akerman 

Turkey 

46 

25 

N. 

SO 

0 

E. 

Alderney I. 

English Channel 

49 

48 

N, 

2 

15 

W. 

Aleppo 

Syria 

35 

45 

N. 

37 

20 

E. 

Alexandretta 

Syria 

36 

35 

N. 

36 

14 

E. 

Alexandria 

Egypt 

31 

13 

N. 

29 

55 

E. 

Algiers 

Africa 

36 

49 

N. 

2 

13 


Alicant 

Spain 

38 

21 

N. 

0 

30 

Ainboyna I. 

Moluccas 

4 

25 

N. 

127 

20 

E. 

Amiens 

France 

49 

53 

N. 

2 

18 

E. 

Amsterdam 

Holland 

52 

22 

N. 

4 

51 

E. 

Amsterdam I. 

Pacific Ocean 

21 

9 

S. 

174 

46 

W 

Ancona 

Italy 

43 

38 

N. 

13 

SO 

E. 

St. Andrews 

Scotland 

56 

21 

N. 

2 

49 


Angers 

France 

47 

28 

N. 

0 

33 

W. 

Angouleme 

France 

45 

39 

N. 

0 

9 

E. 

Angra 

Tercera Azore I. 

38 

39 

N. 

27 

12 

W. 

Annapolis 

Nova Scotia 

44 

52 

N. 

64 

5 

W. 

Antisebes 

France 

43 

35 

N. 

7 

*7 

E- 

Antwerp 

Netherlands 

51 

13 

N. 

4 

23 

E. 

Archangel 

Kussia 

64 

34 

N. 

38 

58 

E. 

Arran I. 

Scotland 

55 

39 

N. 

5 

12 

W. 

Ascension I. 

S. Atlantic 

7 

56 

S. 

14 

21 

W. 

Astracan 

Russia 

46 

21 

N. 

48 

8 

E. 

Athens 

Turkey 

38 

5 

N. 

25 

52 

E. 

St. Augustine 

Madagascar I. 

23 

35 

S. 

43 

8 

E. 

St. Augustine 

East Florida 

SO 

10 

N. 

81 

34 

W. 

Cape St. Augustine 

Brazil 

8 

48 

S. 

35 

5 

W. 

Ava 

Asia 

21 

30 

N. 

96 

0 

E. 

Cape Ava 

Japan 

34 

45 

N. 

140 

55 

E. 

Avignon 

France 

43 

57 

N. 

4 

48 

E. 

Avranches 

France 

B. 

48 

41 

N. 

1 

22 

W, 

Babelmandel Straits 

Red Sea 

12 

50 

N. 

43 

45 

E. 

Babylon (Ancient) 

Syria 

S3 

0 

N. 

42 

46 E. 



longitudes of peaces. 

344 

iVomej of Places, 

(Country or Sea. 

Latitude^, 

O / 

Longitudes. 

0 f 

Bagdat 

Syria 

S3 20 N. 

44 24 E. 

Balasore 

Hindoostan 

21 20 N. 

86 0 E. 

Baltiraore 

Ireland 

51 16 N. 

9 30 W. 

Banca I. (South End) Indian Ocean 

3 15 S. 

107 10 E. 

Banda I. 

Indian Ocean 

4 SO N. 

127 25 E. 

Banff 

Scotland 

57 41 N. 

2 31 wr. 

Bantry Bay 

Ireland 

51 26 N. 

10 10 W. 

Barbadoes I. (Bridge-^-, , - 

town-l ® Canbb. Sea 

13 0 N. 

59 50 W. 

Barcelona 

Spain 

41 23 N. 

2 11 E. 

Basil 

Switzerland 

47 35 N. 

7 29 E. 

Basse Terre 

Gaudaloupe 

15 59 N. 

61 54 W. 

Bastia 

Corsica 

42 42 N. 

9 25 E. 

Batavia 

Java I. 

6 11 S. 

106 52 E. 

Bayonne 

France 

43 29 N. 

1 SO W. 

Bussora OP Bassora Turkey 

SO 45 N. 

47 0 E. 

Beachy Head 

Sussex 

50 44 N. 

0 20 E. 

Belfast 

Ireland 

54 43 N. 

5 57 W,. 

Belgrade 

Turkey 

45 0 N. 

21 20 E. 

Bencoolen 

Sumatra I. 

3 49 S. 

102 10 E. 

Bergen 

Norway 

60 24 N. 

5 20 E. 

Berwick 

Upon Tweed 

55 47 N. 

2 5 W. 

Besancon 

France 

47 14 N. 

6 3 E. 

Bitboa 

Spain 

43 26 N. 

3 23 W. 

Blanco (Cape) 

Africa 

20 55 N* 

17 10 W. 

Blois 

France 

47 35 N. 

1 20 E. 

Bologna 

Italy 

44 29 N. 

11 21 E. 

Bombay I. 

India 

18 57 N. 

72 38 E. 

Boston 

America 

42 25 N. 

70 37 W, 

Botany Bay 

New Holland 

Si 0 s. 

151 23 E. 

Boulogne 

France 

50 43 N. 

1 37 E. 

Bourbon I. 

Indian Ocean 

20 52 S. 

55 SO E. 

BourdeauK 

' France 

44 50 N. 

0 35 W. 

Bremen 

Germany 

53 5 N. 

8 49 E. 

Breslaw 

Silesia 

51 3 N. 

17 9 E. 

Brest 

France 

48 23 N. 

4 29 W. 

Bridlington 

Yorkshire 

54 7 N. 

0 1 W. 

Brighthelmstone 

Sussex 

50 50 N- 

0 5 W. 

Bristol 

Kngland 

51 28 N, 

2 35 W. 

Brunswick 

Germany 

52 30 N. 

10 24 E. 

Brussels 

Netherlands 

50 51 N. 

4 22 E, 

Buccoresti 

Turkey 

44 27 N. 

26 8 E. 

Biida 

Hungary 

47 40 N. 

19 20 B. 

Buenos Ayres 

S. \merica 

34 35 S. 

58 31 W. 

Burgos 

Spain 

c 

42 20 N, 

S 30 W. 

Cadiz or Cales 

Spain 

36 31 N. 

6 12 W, 

Caen 

Franco 

^ 49 11 N. 

0 22 W. 

Cagliari 

Sardinia I, 

39 25 N. 

9 38 E. 

Cairo 

Egypt 

SO 3 N. 

31 21 E. 

Calais 

France 

50 57 N. 

1 51 E. 

Calcutta ' 

Bengal 

22 35 N. 

88 29 E. 

Calmar 

Sweden 

56 40 N. 

16 22 E. 

Cambray 

Netherlandf 

5.0 10 N. 

3 13 E, 


345 


. THE LATITUDES AND 


Names of Places, 

Country or Sea, 

Latitudes, 

o 9 

Longitudes, 

0 9 

Cambridge 

England 

52 n N. 

0 4 B. 

Canary I. (N.E. point) Atlantic 

28 13 N. 

15 39 W. 

Candia 

Candy I. 

S5 19 N. 

25 18 E. 

Canterbury 

England 

51 18 N. 

1 5 E* 

Canton 

China 

23 8 N. 

US 2 E. 

Carlscrona 

Sweden 

56 20 N. 

15 26 E. 

Carthagena 

Spain 

37 37 N. 

1 8 \r. 

Cartbagena 

Terra Firma 

10 27 N. 

75 27 VV. 

Cassel 

Germany 

51 19 N. 

9 35 E. 

Cavan 

Ireland 

54 52 N. 

7 2.) W. 

Cayenne 

I. of Cayenne 

4 56 N. 

3 41 E. 

Chandernagore 

Hindoostan 

22 51 N. 

88 29 E. 

Chartres 

France 

48 2r N. 

1 29 E. 

Cherbourgb 

France 

49 38 N. 

1 37 W. 

Christianna 

Norway 

59 55 N, 

10 48 E. 

Christmas vSound 

Terra del Fuego 

55 ^^2 S. 

70 3 W. 

St. Christopher’s I. 

Caribb. Sea 

17 15 N, 

62 43 W. 

Civita Vecchia 

Italy 

42 5 N. 

11 44 E. 

Clermont 

France 

45 47 N. 

3 5 E. 

Cochin 

India 

9 S3 N. 

75 35 E. 

Colmar 

France 

48 5 N. 

7 22 E. 

Cologne 

Germany 

50 55 N. 

6 55 E. 

Comorin (Cape) 

India 

7 56 N. 

78 5 E. 

Constantinople 

Turkey 

41 1 N 

28 54 E. 

Copenhagen 

Denmark 

55 41 N. 

12 35 E. 

Cork 

Ireland 

51 54 N. 

8 28 W. 

Corvo 

Azores 

39 42 N. 

31 6 \V. 

Contances 

France 

49 1 N. 

1 27 VV. 

Cracow 

Poland 

49 59 N. 

19 50 E. 

Cromartie 

Scotland 

57 43 N. 

4 9 W. 

St. Cruz I. 

Atlantic Ocean 

17 49 N. 

64 53 W. 

Cusco 

Peru 

12 25 S. 

73 35 W. 


D. 



Dantzic 

Poland 

54 22 N. 

18 34 E. 

Dardanelles’s Straits 

Turkey 

40 10 N. 

26 26 E. 

Dartmouth 

England 

50 21 N. 

3 42 W. 

Delhi 

Hindooston 

28 37 N. 

77 40 E. 

Deseada I. 

Caribb. Sea 

16 36 N. 

61 10 W. 

St. Dennis 

Isle Bourbon 

20 52 S. 

55 30 E. 

Dieppe 

France 

49 45 N. 

1 4 E. 

Dingle Bay 

Ireland 

51 55 N. 

10 40 W. 

St. Domingo 

Caribb Sea 

18 20 N. 

69 46 TT. 

Dort 

United Provinces 

51 47 N. 

4 35 E. 

Douglass 

Isle of Man 

54 7 N. 

4 38 W. 

Dover 

England 

51 8 N. 

1 18 E. 

Drontheim 

Norway 

63 26 N. 

10 22 E. 

Dublin 

Ireland 

53 21 N. 

6 6 W. 

Dunisar 

Scotland 

56 1 N. 

2 33 W. 

Dundee 

Scotland 

56 28 N. 

2 58 W. 

Dungarvon 

Ireland 

52 0 N. 

7 50 W, 

Dungeness 

England 

50 52 N. 

0 59 E. 

Dunkirk 

France 

51 2 N. 

2 22 E. 

Durham 

England 

54 44 N. 

1 15 W, 

Durazzti 

Turkey 

41 58 N. 

25 0 E. 


JVames of Places. 

East Cape 

Eddystone Light 

Edinburgh 

Elbing 

Elsinore 

Einbden 

Enibrun 

Enliesus 

Erzerum 

Evustatia 

Evreux 

Exeter 

Fair Island 
Falmouth 
FaLe Bay 
Farewt^II (Cape) 
Fayal l uwa 
Fern Lland 
Ferrara 

Ferro Island (Town) 
Ferrol 

Finisterre (Cape) 
Flamborougli Head 
Florence 
Flores 

Florida (Cape) 
Flushing 
N. Forelatid 
Fortaventura, W.poin 
Fort rose 
Foulness 
France (fsle of) 
Franco's (Cape) 
Fraiikl'oit (on the 
Main) 

Futichal 

Furneaux Island 

Gap 

Galway 

Geneva 

Genoa 

St. Geortre (Town) 

Fort ‘t. George 

Glient 

Gibraltar 

Glasgow 

Goa I. 

G<jiiiera 1. 

Good Hope (Cape) 
Guree t. 

Gottenbnrg 
Gottingen (Obser.) 


LOXGITUDES OF PLACES. 34^ 


(Jountry or Sea. 

Latiludes. 

Longitudes. 

New Zealand 

Q 

S7 

/ 

42 

S. 

O 

174 

SO 

W. 

England 

50 

8 

N. 

4 

24 

w. 

Scotland 

55 

58 

N. 

3 

12 

w. 

Poland 

54 

12 

N. 

20 

35 

E. 

Denmark: 

56 

2 

N. 

12 

37 

E. 

Germany 

53 

12 

N. 

7 

16 

E. 

France 

44 

34 

N. 

6 

29 

E. 

Turkey in Asia 
Turkey in Asia 

38 

0 

N. 

27 

53 

E. 

39 

56 

N. 

48 

35 

E. 

Caribb. Sea 

IT 

SO 

N. 

63 

14 

W. 

France 

49 

1 

N. 

1 

9 

E. 

England 

50 

44 

N. 

3 

34 

W. 

F. 







Orkney Islands 

59 

30 

N. 

1 

46 

W. 

England 

50 

8 

N. 

5 

2 

W. 

Cape of Good'Hope 

34 

to 

S. 

18 

33 

E. 

Greenland 

59 

SO 

N. 

42 

42 

W. 

Azore Islands 

38 

32 

N. 

28 

41 

W, 

England 

55 

38 

N. 

1 

44 

\V. 

Italy 

Canary Isles 

44 

50 

N. 

11 

36 

E. 

27 

47 

N. 

17 

46 

W. 

Spain 

43 

29 

N 

8 

15 

W. 

Spain 

42 

52 

N. 

9 

17 

\V. 

England 

54 

11 

N. . 

0 

19 

E. 

Italy 

43 

46 

N. 

11 

2 

E. 

Aijiiie [^lands 

39 

34 

N. 

31 

0 

W. 

S. America 

25 

47 

N. 

80 

35 

W. 

United Prov'^. 

51 

27 

N. 

3 

33 

E. 

England 

L Canary Isles 

51 

t5 

N. 

1 

28 

E. 

28 

4 

E. 

14 

31 

VV. 

Scotland 

57 

40 

N. 

4 

7 

vr. 

Eng*aj;d 

52 

57 

N. 

0 

55 

E. 

Indian Ocean 

20 

21 

S. 

57 

16 

E. 

St. Domingo 

19 

46 

N. 

-12 

18 

w. 

Germany 

49 

55 

N. 

8 

35 

E. 

1. of Madeira 

qo 

.88 

N. 

IT 

6 

\V. 

Society Isles 

17 

li 

S. 

143 

•7 


G. 







France 

44 

S3 

N. 

6 

5 

E. 

Ireland 

53 

10 

N. 

10 

1 

W. 

Switzerland 

46 

12 

N. 

6 

0 

E. 

Italy 

44 

25 

N. 

8 

36 

E. 

Bermudas I. 

32 

22 

N. 

64 

.53 

VV. 

Or Madras 

13 

5 

N 

80 

29 

E. 

Netherlands 

51 

5 

N. 

3 

44 

E. 

Spain 

56 

5 

N. 

5 

22 

VV. 

Scotland 

55 

52 

N. 

4 

15 

VV. 

Malabar Coast 

15 

51 

N. 

73 

45 

E. 

Canary Isles 

28 

6 

N. 

17 

o 

<> 

TV. 

Africa 

54 

29 

s. 

18 

23 


Africa 

14 

10 

N. 

17 

25 

VV. 

Sweden 

57 

42 

N. 

It 

39 

E. 

(iermany 

51 

32 

N. 

9 

53 

E. 


iT) 


347 

THE LATITUDES 

AND 


Names of Platts. 

Country or Sea. 

Latitudes. 

e t 

Longiii 

o f 

Granville, 

France 

48 50 N. 

1 37 

Graciosa 

Azore Islands 

39 2 N. 

27 58 

Gravelines 

France 

50 59 N. 

2 7 

Gratz 

Germany 

47 4 N. 

15 26 

Gravesend 

England 

51 28 N. 

0 20 

Greenwich (obs.) 

England 

51 29 N. 

0 0 

Guadeloupe 

Caribb. 1. 

15 59 N. 

61 59 

Guernsey 

English Channel 

49 SO N. 

2 52 


H. 



Haerlem 

United Prov. 

52 22 N. 

4 36 

Hague 

United Prov. 

52 4 N. 

4 17 

Halifax 

Nova Scotia 

44 46 N. 

63 27 

Hamburgh 

Germany 

53 34 N. 

9 55 

Hanover 

Germany 

52 22 N. 

,9 48 

Harwich 

England 

52 11 N. 

1 13 

Hatteras (Cape) 

N. America 

35 12 N. 

76 5 

Havre de Grace 

France 

49 29 N. 

0 6 

Havannah 

Isle of Cuba 

23 12 N. 

82 18 

St Helena (James 
Town) 

1 Atlantic 

15 55 S. 

5 49 


Hervey’s I. 

La Hogue (Cape) 
Holyhead 
Horn (Cape) 

Hull 

Jackson (Port)- 
Jatfa 

Jackutskoi 
Janeiro (Rio) 
JaNsy 

Java Head 

Jeddo 

Jerusalera 


Society Isles 
France 
Wales 
S. America 
England 

I. & 

New Holland 
Syria 
Siberia 
Brazil 
Jurkey 
I. of Java 
I. of Japan 
Syria 

Jersey Isle (St- Aubins) Eng Channel 


Ingolstadt 
Inverness 
Joannah 
St. .Tohn^s 
St. Josephus 
Islamabad 
Ispahan 

Jodda, or Gidda 
St. Julian (Port) 
Juan Fernandez 

JIaratschatka 

JH.Kilda 

Kinsale 

Kiow 

Kola 

Konsingsberg 


Germany 
Scotland 
Comora Isles 
Newfoundland 
California 
Hindoostan 
Persia 
Arabia 
Patagonia 
Pacific Ocean 

K. 

Siberia 

Hebrides 

Ireland 

Russia 

Lapland 

Prussia 


19 17 S. 
49 45 N. 
53 23 N. 
55 58 S. 
53 48 N. 

S3 52 S- 
32 5 N. 
62 1 N. 

22 54 S. 
47 8 N. 
6 49 S. 
36 0 N. 
Si 46 rv. 
49 13 N. 
4*^ 46 N. 
57 36 N. 
12 5 N. 
47 32 N. 

23 4 N. 
22 20 N. 
32 52 N. 
21 29 N. 
49 10 N. 
S3 45 N. 


158 48 

1 57 
4 45 

67 26 
0 S3 

15! 19 

35 10 
129 48 
42 44 
27 SO 
105 14 
139 40 
35 20 

2 12 
11 22 

4 15 
45 40 
52 26 
109 42 
91 45 
52 50 
39 22 

68 44 
78 37 


E. 

E. 

E. 

E. 

W. 

E. 

W. 

E. 

W. 

W. 

E. 

E. 

E. 

W. 

W. 


56 20 N. 163 0 E. 

57 47 N. 8 40 W. 


51 32 N. 
50 27 N. 
68 52 N. 
54 43 N. 


8 50 W. 
SO 27 E. 
33 1 E. 
21 35 E. 




LONGITUDES OF PLACES. 318 


Nam&s of Places. 

Country or Sea, 

h. 

latitudes, 

0 f 

Longitudes^ 
0 / 

Ladrone (I. Guam.) 

Pacific Ocean 

13 10 

N. 

143 15 

E. 

Laodau 

France 

A9 11 

N. 

8 7 

E. 

lJas^a 

Thibet 

SO 12 

N. 

91 20 

E, 

Landscroon 

Sweden 

55 52 

N. 

12 50 

E. 

Land's End 

England 

50 4 

N. 

5 41 

W. 

Laa>uune 

Switzerland 

46 31 

N. 

6 45 

E. 

Leeds 

England 

53 48 

N. 

1 34 W. 

Legiiorn 

Italy 

4S sS 

N. 

10 16 

E. 

Leitu 

Scotland 

56 0 

N. 

3 11 

E. 

Leipsic 

Germany 

51 19 

N. 

12 20 

E, 

Leyden 

United Prov. 

52 8 

N. 

4 28 

E. 

Lerwick, or Leerwick Shetland Isles 

€0 13 

N. 

0 55 

W, 

Lie^e 

Netherlands 

50 S7 

N. 

5 35 

E. 

Lima 

Peru 

12 1 

S. 

76 49 

W. 

Limerick 

Ireland 

52 22 

N. 

9 53 W. 

Limoges 

France 

45 50 

N. 

1 16 

E, 

Lintz 

Germany 

48 16 

N. 

13 57 

E. 

Lisle 

Netherlands 

50 38 

N. 

3 4 

E. 

Lisbon 

Portugal 

38 40 

N. 

9 10 

W. 

Liverpool 

England 

53 24 

N. 

3 12 

w. 

Lizard 

England 

49 57 

N. 

5 11 

w. 

London (St. PauPs) 

England 

51 31 

N. 

0 6 

w. 

LouisburgU 

I. of Cape Breton 

45 54 

N. 

59 54 

w . 

Louvain 

Netherlands 

50 53 

N. 

4 44 

E. 

St. Lucia 

Caribb. Sea 

13 24 

N. 

60 51 

w. 

Lunden 

Sweden 

55 42 

N. 

13 2 

E. 

Luneville 

F ranee 

48 35 

N. 

6 30 

E. 

Luxembourg 

N etherlands 

49 37 

N. 

6 12 

E. 

Lynn 

England 

France 

M. 

52 45 

N. 

0 23 

E. 

Lyons 

45 46 

N. 

4 48 

E. 

Macao 

China 

22 13 N. 

113 46 

E. 

Macassar 

1. of Celebes 

5 9 

S. 

119 49 

E. 

Madeira t. (Funchal) Atlantic 

32 38 

N. 

17 6 

W. 

jNladras 

India 

13 5 

N. 

80 29 

E, 

Madrid 

Spain 

40 25 

N. 

3 l2 

W. 

Mahon (Port) 

Minorca 

39 51 

N. 

3 48 

E. 

Majorca I. 

Mediterranean 

39 35 

N. 

2 SO 

E. 

Malacca 

India 

2 12 

N. 

102 5 

E. 

Malines, or Mechlin 

Netherlands 

51 2 

N. 

4 29 

E. 

St Malo 

France 

48 39 

N. 

2 2 

W. 

Malta 

Mediterranean 

35 54 

N. 

14 28 

E. 

Ma ilia 

Phillippinelsland 

14 36 

N. 

120 53 

E. 

Marigalante I. 

Caribb. Sea 

15 55 

N. 

61 11 

W. 

Marseilles 

France 

43 18 

N. 

5 22 

E. 

Martinico 

Caribb. Sea 

14 44 

N. 

61 21 

W. 

Mayence, or Mentz 

Germany 

49 54 

N. 

8 20 

E. 

Mayo I. 

Cape Verd Is. 

15 10 

N. 

23 5 

W. 

Mecca 

Arabia 

21 40 

N. 

41 0 

E. 

Mexico 

America 

19 26 

N. 

loe 6 

W. 

Milan 

Italy 

45 28 

N. 

9 12 

E. 

Minorca 

Mediterranean. 

39 51 

N. 

3 54 

E. 

Mocha 

Arabia 

13 44 

N. 

44 4 

K. 


349 

THE LATITUDES AND 




Na7nes of Places. 

Country or Sea. 

Latitudes. 

o r 

Longiiudes 

o / 

Mndena 

Italy 

44 S4 

N. 

11 12 

E 

Mont(;elier 

Prance 

43 ST 

N. 

3 53 

E. 

Montreal 

Canada 

45 50 

N. 

73 11 

W. 

Moscow 

Russia 

55 46 

N. 

37 33 

E. 

Munich 

Germany 

N. 

48 10 

N. 

11 SO 

E. 

Namur 

Netherlands 

50 28 

N. 

4 46 

E. 

Nancy 

Fiance 

48 42 

N. 

6 10 

E. 

Nankin 

China 

32 5 

N. 

118 46 

E. 

Nantes 

France 

47 13 

N. 

1 34 

W. 

Naples 

Italy 

40 50 

N. 

14 17 

E. 

Narbonne 

France 

43 11 

N. 

3 0 

E. 

Naze 

Norway 

57 58 

N. 

7 3 

E. 

N ew-castle-upon-TyneEngland 

55 3 

N. 

1 30 

\V. 

N iagara 

Canada 

43 4 

N. 

79 8 

W. 

Nice 

France 

43 42 

N. 

7 17 

E. 

Nieuport 

Flanders 

51 8 

N. 

2 45 

E. 

Nismes 

France 

43 50 

N. 

4 19 

E. 

Norfolk I. 

New Holland 

29 2 

S. 

168 10 

E. 

North CapB 

Lapland 

71 30 

N. 

25 57 

E. 

Nuremberg 

Germany 

0. 

49 2T 

N. 

11 4 

E. 

Ockzakow 

Russia 

45 12 

N. 

34 40 

E. 

Oeland 1. (S, end) 

Sweden 

56 15 

N. 

18 35 

E. 

Oleron I. 

France 

46 3 

N. 

1 25 

W. 

St. Oiner 

Netherlands 

50 45 

N. 

2 15 

E. 

Oporto 

Portugal 

41 10 

N.' 

8 27 

W. 

Orbitello 

Italy 

42 32 

N. 

12 .7 

E. 

Orleans (New) 

Louisiana 

29 58 

N. 

89 59 

W. 

Ortegal (Cape) 

Spain 

43 46 

N. 

7 39 

W. 

Osnaburg I. 

Society Is. 

17 52 

S. 

148 6 

W. 

Ostend 

Netherlands 

51 14 

N. 

2 56 

E. 

O’why’hee (N. end) 

Sandwich Is. 

18 54 

N. 

155 45 

W. 

Oxford (observ.) 

England 

P. 

51 45 

N. 

1 15 

W. 

Padua 

Italy 

45 14 

N. 

11 52 

E. 

Palermo 

Sicily 

38 10 

N. 

13 42 

E. 

Palma I. 

Canary Islands 

28 37 

^N. 

17 50 

W. 

Panama 

IMexico 

8 48 

N, 

80 21 

W. 

Paris (observ.) 

France 

4« 50 

N. 

2 20 

E. 

Pegu 

India 

17 0 

N. 

96 .58 

E. 

Pekin 

China 

39 54 

N. 

116 27 

E. 

Perigueux 

France 

45 11 

N. 

0 43 

E. 

Perpignan 

France 

42 42 

N. 

2 54 

E. 

Peterhead 

Scotland 

57 32 

N. 

1 46 

W. 

Petersburg 

Russia 

59 56 

N. 

30 19 

E. 

Philadelphia 

America 

39 57 

N. 

75 IS 

\V. 

Pico i. 

Azure Is. 

38 29 

N, 

28 26 

W. 

Pisa 

Italy 

43 43 

N. 

10 23 

E. 

Plymouth 

England 

50 22 

N. 

4 16 

W. 

Poitiers 

France 

46 .35 

N. 

0 21 

E. 

Pondicherry 

India 

11 42 

N. 

79 53 

E. 

Port Glasgow 

Scotland 

55 56 

N. 

4 38 

W. 

Portland (lighthouse) England 

50 31 

N. 

2 27 

W. 


LONGirCDES OF PL ACES. 


JVames of Places. 

Porto Eello 

Port KoyaJ 

Portsmouth 

Pragtje 

Piesburg 

Providence 

Quebec 

Queda 

Quimper. 

St. Q,P)intin 
Quiros (Cape) 
Quito 

Eamhead 
- Ramsby 
Hamsgate 
Ravenna 
R ennes 
Rbeims 
Rhodes (I, of) 
I^hode Island 
Riga 
Rochelle 
Rochester 
Rome 
Roth say 
Rotterdam 
Rouen 
Kugen I. 

Rye 

Salerno 
Sal i.s bury 
Sail 1. 

Salle 
Samana 
Samarcand 
Samos I. 

Santa Cruz 

Sandwich 

Saratov 

Sav'annah 

Scanderoon 

Scarborough 

Scaw Light 

Schelling 1 . 

Schirauz 

Scilly Isles 

Sedan 

Senegal 

Siam 

Smyrna 

Southampton 


Country or Sea. 

America 

Jamaica 

England 

Bohemia 

Hungary 

America 

Q. 

Canada 

Malacca 

France 

France 

IN'ew Hebrides 

Peru 

R. 

Cornwall 

Isle of Man 

England 

Italy 

France 

France 

Archipelago 

America 

Russia 

France 

England 

Italy 

Isle of Bute 
United Provinces 
France 
Baltic 
England 

s. 

Italy' 

England 

Cape Verd Is. 

Morocco 

St. Domingo 

W. Tartaiy 

Archipelago 

Tenerifte 

England 

Russia 

N. America 

Syria 

FJngland 

Denmark 

United Prov. 

Fap. of Persia 

English Channel 

France 

Africa 

India 

Natolia 

England 


Latitudes'. 

0 3S N. 
18 0 N 
50 47 N. 
50 5 N. 
48 8 N. 
41 51 N. 


46 55 N. 
6 15 N. 

47 58 N. 
49 51 N. 
14 56 S. 

0 13 S. 


50 19 N, 

54 17 N. 

51 N. 
44 N. 

48 7 JN. 

49 lb N. 
35 27 N. 
41 28 iN. 
57 5 N. 
46 9 N. 
51 26 N. 
41 54 N. 

55 50 N. 
5i 56 i\. 

49 27 N. 
54 42 N. 

50 55 jV. 


40 E9 N. 
51 4 N. 

16 .58 N. 
24 10 N. 
19 15 N. 
39 45 N. 
37 46 N, 

28 27 N. 
51 19 N. 
51 SO M. 
32 3 N. 
36 35 N. 
54 21 N. 
57 44 N. 
53 17 JM. 

29 40 X. 
49 56 X. 

49 42 X. 
15 56 X. 
14 18 X. 
Si) 21J X. 

50 r , r , M. 


3.50 


rjoni^itudcs. 

o / 

79 50 4V. 
76 45 W. 

1 6 W, 
14 24 E. 
17 S3 E. 
71 26 W. 


69 53 47. 
100 12 E. 
4 7 W. 
3 17 E. 
167 20 E. 
77 55 W. 


4 20 W. 
4 26 W. 
1 24 E. 
12 0 E. 
1 42 W. 

4 2 E. 
28 45 E. 
71 30 W. 
25 5 E. 

1 10 

0 .50 E. 
12 29 E. 

5 17 W. 
4 28 E. 
1 5 

14 30 E. 
0 44 E. 


14 48 E. 
1 47 

22 56 \r. 
6 43 W. 
69 16 W. 
63 20 E. 
27 13 E. 
16 16 W. 
1 15 E. 
46 0 E. 
81 24 W. 
36 14 E. 

0 18 W. 
10 37 E. 

5 7 E. 
54 SO E. 

6 46 W. 
4 57 E. 

16 21 \V. 
100 50 E. 
27 20 E. 

1 5 W. 


THE LATITUDES AND 


351 

Names of Placesr, 

Start Point 

Stockholm 

Stockton 

Strasburg 

Stralgund 

Suez 

Surat 

Surinam 

Swansea 

Syracuse 

Tamarin Town 
Tangier 
Tarento 
Tenetios I. 
Teneriflfe (Peak) 
Tereera I. 

Texel I. 

Thionville 

Tobolsk 

U'chago It 

Toledo 

Tomsk 

Torbay 

Tornea 

Toulouse 

Trieste 

Trincomal© 

Tripoli 

Troyes 

Tuiin 

Uliateah 

Upsal 

Uraniburgli 

Ushant 

Valenciennes 

Valencia 

Vannes 

Venice 

Vera Cruz 

Verd (Cape) 

Verdun 

Verona 

Versailles 

Vienna (obser.) 

Vigo 

Vincent (Cape) 
Vintiraiglia 
Virgin iiorda 

Wakefield 

Wardhuys 


Country or Sea, 

Latitudes* 

a r 

Longitudes, 

o t 

England 

50 9 

N. 

3 

51 

Wt 

Sweden 

59 t\ 

N. 

18 

4 

K. 

England 

54 41 

N. 

1 

9 

W. 

France 

48 5 

N. 

7 

45 

E. 

Germany 

54 23 

N. 

14 

10 

B. 

Africa 

29 5o 

N. 

S3 

27 

E. 

India 

21 10 

N. 

72 

22 

E. 

S. America 

6 30 

N. 

55 

SO 

W. 

Wales 

51 40 

N. 

4 

30 

W. 

Isle ot bicily 

37 4 

N. 

15 

St 

E. 

T. 






Isle of Socotra 

12 So 

N. 

53 

9 

E. 

Coast of Darbary 

35 55 

N. 

5 

45 

W. 

Italy 

40 43 

N 

17 

31 

E. 

Archipelago 

39 57 

N 

26 

14 

E. 

Canary Islands 

28 13 

N. 

16 

29 

W. 

Az>>rf- i^^lands 

3H 4-> 

N. 

27 

6 

W. 

United Prov. 

53 10 

N. 

4 

59 

E. 

France 

49 21 

N. 

6 

'.j 

E. 

Siberia 

58 12 

N. 

68 

25 

E. 

Canbb. Sea 

11 la 

N. 

6o 

27 

W. 

Spain 

39 50 

N. 

3 

20 

W. 

Siberia 

56 .30 

N. 

84 

59 

E. 

English Channel 

50 S3 

N, 

3 

42 

w. 

Lapland 

65 5l 

N. 

24 

12 

E. 

France 

43 36 

N. 

1 

26 

E. 

Adriatic Sea 

45 51 

N. 

14 

3 

E. 

Isle of Ceylon 

8 32 

N. 

81 

11 

E. 

Barbary 

32 54 

N. 

13 

5 

E. 

F ranee 

48 18 

N. 

4 

5 

E. 

Piedmont 

45 4 

N. 

7 

40 

E. 

U. & V. 






Society Islands 

16 45 

S. 

151 

31 

W. 

Sweden 

59 52 

N. 

17 

42 

E. 

Denmark 

55 54 

N. 

12 

52 

E. 

Coast of France 

48 28 

N. 

5 

4 

W. 

France 

50 2l 

N. 

3 

32 

E. 

Spain 

39 30 

N. 

0 

40 

W. 

France 

47 39 

N. 

2 

46 

W. 

Italy 

45 26 

N. 

12 

4 

E. 

Mexico 

19 12 

N. 

97 

20 

W. 

Africa 

F ranee 

14 45 
49 9 

N. 

N. 

17 

5 

33 

23 

W, 

E. 

Italy 

45 26 

N. 

11 

18 

E. 

France 

Austria 

48 48 
48 12 

N. 

N. 

2 

16 

T 

16 

E. 

E. 

Spain 

42 14 

N. 

8 

28 

W. 

Spain 

37 3 

N. 

8 

59 

W. 

Italy 

43 53 

N. 

7 

37 

E. 

West Indies 

18 18 

N. 

64 

0 

W. 

w. 




England 

53 41 

N. 

1 

33 

W. 

Lapland 

70 23 

Nt 

31 

7 

E. 


LONGITUDES OF PLACES. 352 


iVames of Places. 

Country or Sea. 

Latitudes. 

o / 

Longitudes. 
0 ^ 

Warsaw 

Poland 

52 14 

N. 

21 0 E. 

Washington 

N. America 

38 53 

N. 

77 43 W. 

W’exford 

Ireland 

52 22 

N, 

6 30 W- 

Weymouth 

England 

52 40 

N. 

2 34 W. 

Whitehaven 

England 

54 25 

N, 

3 23 W. 

Wihia 

Poland 

51 41 

N. 

25 27 E. 

Wittenburg 

Germany 

51 53 

N. 

12 24 E. 

Worcester 

England 

52 9 

N. 

2 0 W. 

Wurtzburg 

Germany 

49 46 

N. 

10 14 E. 

Wyburg 

Kussia 

60 55 

N. 

SO 20 E. 


Y. 




Yarmouth 

England 

52 55 

N. 

1 40 E. 

York 

England 

53 59 

N. 

1 7 W. 

York (New) 

N. America 

40 43 

N. 

74 10 W. 

Y^oughall 

Ireland » 

51 48 

N. 

8 0 W. 



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